203 + Interview Questions in DEFINITE-INTEGRAL IN GENERAL AWARENESS Page 3 InterviewSolution

101.	If `int_(a)^(b)f(x)dx=int_(a)^(b)phi(x)dx`, then-A. `f(x)=phi(x)`B. `f(x)-phi(x)=c`C. `f(x)+phi(x)=c`D. none of these
Answer» Correct Answer - D

Discussion

102.	The value of `int_(0)^(pi)sinthetad theta` is-
Answer» Correct Answer - C

Discussion

103.	`int_(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x + cos^(4)x)dx=`A. `pi/2`B. `pi/4`C. `(3pi)/2`D. `(3pi)/4`
Answer» Correct Answer - A

Discussion

104.	`int_(-pi//2)^(pi//2)sin^(2)xdx`A. `pi/2`B. `pi/4`C. `pi/2-1/4`D. `pi/4-1/2`
Answer» Correct Answer - A Let I = \(\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\) \(\because\) sin²(-x) = (-sin x)² = sin²x \(\therefore\) I = 2 \(\int\limits^{\frac{\pi}2}_0\) sin²x dx = \(\cfrac{2\,\Gamma(\frac{2+1}{2})\,\Gamma(\frac{0+1}{2})}{2\,\Gamma\,(\frac{2+0+2}{2})}\) = \(\cfrac{\Gamma(\frac32)\,\Gamma(\frac12)}{\Gamma(2)}\) = \(\cfrac{\frac12\,\Gamma(\frac12)\,\Gamma(\frac12)}{1!}\) (\(\because\Gamma(\frac32) = \frac12\Gamma(\frac12)\)) = \(\frac12\sqrt{\pi}.\sqrt{\pi}\) (\(\because\Gamma(\frac12)= \sqrt{\pi}\)) = \(\frac{\pi}2\)

104.

`int_(-pi//2)^(pi//2)sin^(2)xdx`A. `pi/2`B. `pi/4`C. `pi/2-1/4`D. `pi/4-1/2`

Answer» Correct Answer - A

Let I = \(\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\)

\(\because\) sin²(-x) = (-sin x)² = sin²x

\(\therefore\) I = 2 \(\int\limits^{\frac{\pi}2}_0\) sin²x dx

= \(\cfrac{2\,\Gamma(\frac{2+1}{2})\,\Gamma(\frac{0+1}{2})}{2\,\Gamma\,(\frac{2+0+2}{2})}\)

= \(\cfrac{\Gamma(\frac32)\,\Gamma(\frac12)}{\Gamma(2)}\)

= \(\cfrac{\frac12\,\Gamma(\frac12)\,\Gamma(\frac12)}{1!}\) (\(\because\Gamma(\frac32) = \frac12\Gamma(\frac12)\))

= \(\frac12\sqrt{\pi}.\sqrt{\pi}\) (\(\because\Gamma(\frac12)= \sqrt{\pi}\))

= \(\frac{\pi}2\)

Discussion

105.	If `altcltb` then `int_(a)^(b)f(x)dx` is equal to-A. `int_(a)^(c)f(x)dx+int_(b)^(c)f(x)dx`B. `int_(a)^(c)f(x)dx-int_(c)^(b)f(x)dx`C. `int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx`D. `int_(c)^(a)f(x)dx-int_(b)^(c)f(x)dx`
Answer» Correct Answer - C

Discussion

106.	`int_(0)^(na)f(x)dx=nint_(0)^(a)f(x)dx` if-A. `f(a-x)=f(x)`B. `f(n+x)=f(x)`C. `f(n-x)=f(x)`D. `f(a+x)=f(x)`
Answer» Correct Answer - D

Discussion

107.	If `f(2a-x)=-f(x)` then `int_(0)^(2a)f(x)dx` is equal to-A. `int_(0)^(a)f(x)dx`B. 0C. `int_(-a)^(a)f(x)dx`D. 1
Answer» Correct Answer - B

Discussion

108.	`int_(-(pi)/(2))^((pi)/(2))cosxdx`A. 2B. 1C. 0D. `(1)/(2)`
Answer» Correct Answer - A

Discussion

109.	`lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))}` is equal to-A. `(pi)/(2)`B. `sin^(-1)(1)`C. `cos^(-1)0`D. `2tan^(-1)(1)`
Answer» Correct Answer - A::B::C::D

Discussion

110.	`int_(pi//3)^(pi//2) dx/(sinx+ sin 2x)=`A. `2/3 log 2- 1/2 log 3`B. `4/3 log 2 - 1/2 log 3 `C. `2/3 log 2 - 3/2 log 3 `D. `4/3log 2- 3/2log 3`
Answer» Correct Answer - B

Discussion

111.	`int_(0)^(pi//2) (cosx)/((1+sin x)(2+sin x) ) dx = `A. `log (2/3)`B. `log(3/2)`C. `log(4/3)`D. `log(3/4)`
Answer» Correct Answer - C

Discussion

112.	`int_(0)^(pi//2) (1+ 2 cos x)/((2+ cosx )^(2) )dx = `A. `pi`B. `2`C. `pi/2`D. `1/2`
Answer» Correct Answer - D

Discussion

113.	`int_(0)^(pi//2) (cosx)/((4+sin x)(3+sin x) ) dx = `A. `log (16/15)`B. `log(15/16)`C. `log (4/15)`D. `log(15/4)`
Answer» Correct Answer - A

Discussion

114.	`int_(pi//4) ^(3pi//4) dx/((sin x - 2 cosx)(2sin x + cos x))=`A. `1/5 log 3`B. `1/5 log 9`C. `5 log 3`D. `5 log 9`
Answer» Correct Answer - B

Discussion

115.	`int_(0)^(pi//2) sin ^(3) x cos^(3) x" "dx = `A. `1/12`B. `1/24`C. `1/3`D. `1/6`
Answer» Correct Answer - A

Discussion

116.	`int_(2)^(3)x^(2)dx`A. `211/5`B. `(-211)/5`C. 55D. -55
Answer» Correct Answer - A

Discussion

117.	Let `f(x)=sin^(4)x-cos^(4)xandg(x)=1-2sin^(2)xcos^(2)x`. `intg(x)dx`=A. `(3x)/(4)-(cos4x)/(16)+c`B. `(3x)/(4)+(sin4x)/(16)+c`C. `(3x)/(4)-(sin4x)/(16)+c`D. `(3x)/(4)+(sin4x)/(8)+c`
Answer» Correct Answer - B

Discussion

118.	Which of the following is true ?A. `int_(0)^(1) sqrt(x)" " dx=2/3`B. `int_(0)^(1) sqrt(x)" " dx=(-2)/3`C. `int_(0)^(1) sqrt(x)" " dx=3/2`D. `int_(0)^(1) sqrt(x)" " dx=(-3)/2`
Answer» Correct Answer - A

Discussion

119.	`int_(0)^(pi//2) sin ^(2) x cos^(3) x" "dx = `A. `pi`B. 0C. `pi/2`D. `pi/4`
Answer» Correct Answer - B

Discussion

120.	Evaluate the following : `int_(0)^(1)(1-x^(2))/(1+x^(2))dx`A. `pi/2 - 1`B. `pi/2+ 1`C. `pi/4 -1`D. `pi/4 +1`
Answer» Correct Answer - A

Discussion

121.	`int_(4)^(9) dx/sqrt(x) =`A. 1B. -2C. 2D. -1
Answer» Correct Answer - C

Discussion

122.	`int_(4)^(7)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=`A. `(-11) / 2`B. `11/ 2`C. `(-3)/2`D. `3/2`
Answer» Correct Answer - D

Discussion

123.	`int_(0)^(1//sqrt(2))(sin^(-1)x)/((1-x^(2))^(3//2))dx=?`A. `pi/4+1/2log2`B. `pi/4-1/2log2`C. `pi/2+1/4log2`D. `pi/2-1/4log2`
Answer» Correct Answer - B

Discussion

124.	Evaluate the following : `int_(0)^(1)(x^(2)-2)/(x^(2)+1)dx`A. `1+pi/4`B. `1-pi/4`C. `1+(3pi)/4`D. `1-(3pi)/4`
Answer» Correct Answer - D

Discussion

125.	Prove that `int_(a)^(b)(f(x))/(f(x)+f(a+b-x)) dx=(b-a)/(2)`.A. `(b-a)/2`B. `(b-a)/4`C. `(b+a)/2`D. `(b+a) /4`
Answer» Correct Answer - A

Discussion

126.	`int_(2)^(7) sqrt(x)/ (sqrt(x) + sqrt(9-x))dx=`A. `9/2`B. `(-9)/2`C. `5/2`D. `(-5)/2`
Answer» Correct Answer - C

Discussion

127.	`int_(0)^(1) (x^(2) + 3x+2)/sqrt(x) dx=`A. `8/5`B. `16/5`C. `32/5`D. `64/5`
Answer» Correct Answer - C

Discussion

128.	`If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx.` thenA. `I = J`B. `IltJ`C. `IgtJ`D. `I+J=pi/4`
Answer» Correct Answer - D

Discussion

129.	`int_(-pi) ^(pi) (sin^(4) x) / (sin ^(4) x + cos^(4)x)dx=`A. `pi`B. `2pi`C. `pi/2`D. `(3pi)/2`
Answer» Correct Answer - A

Discussion

130.	`int_(1)^(2) sqrt(x)/ (sqrt(3-x) + sqrt(x))dx=`A. `(-1)/2`B. `1/2`C. `3/2`D. `(-3)/2`
Answer» Correct Answer - B

Discussion

131.	`int_(0)^(1) (dx)/(sqrt(1+x)sqrt(x))=`A. `2/3 (sqrt(2)-1)`B. `2/3(sqrt(2)+1)`C. `4/3(sqrt(2)-1)`D. `4/3(sqrt(2)+1)`
Answer» Correct Answer - C

Discussion

132.	`int_(0)^(1) x^(2)/(x^(2)+1)dx=`A. `2 - pi /4`B. `2 + pi/4`C. `1-pi/4`D. `1+pi/4`
Answer» Correct Answer - C

Discussion

133.	`int_(0)^(pi//2)cos^(2) x" "dx=`A. `(3pi)/4`B. `pi/4`C. `(3pi)/2`D. `pi/2`
Answer» Correct Answer - B

Discussion

134.	Evaluate the following : `int_(0)^(1)(1)/(sqrt(3+2x-x^(2)))dx`A. `pi/4`B. `pi/2`C. `pi/6`D. `pi/12`
Answer» Correct Answer - C

Discussion

135.	Evaluate: `int_0^2(5x+1)/(x^2+4)dx`A. `5/2 log 2 - pi/4`B. `5/2 log 2 +pi/4`C. `5/2 log 2 -pi/8`D. `5/2 log 2 +pi/8`
Answer» Correct Answer - D

Discussion

136.	`int_(3)^(5) (dx)/(sqrt(x+4)+sqrt(x-2))=`A. `1/9 (28-3sqrt(3) - 7 sqrt(7))`B. `1/9 (28-3sqrt(3) + 7 sqrt(7))`C. `1/9 (28+3sqrt(3) -7 sqrt(7))`D. `1/9 (28+3sqrt(3) +7 sqrt(7))`
Answer» Correct Answer - A

Discussion

137.	Evaluate the following : `int_(1)^(2)(dx)/(x^(2)+6x+5)`A. `1/4 log (9/7)`B. `1/4 log (7/9)`C. `1/2 log (3/7)`D. `1/2 log (7/3)`
Answer» Correct Answer - A

Discussion

138.	`int_0^a(dx)/(sqrt(a x-x^2))`A. `pi/2`B. `pi/4`C. `pi`D. 0
Answer» Correct Answer - C

Discussion

139.	Evaluate the following : `int_(0)^(pi//4)sin 3x sin 2x dx`A. `(3sqrt(2))/5`B. `(2sqrt(2))/5`C. `3/(10 sqrt(2))`D. `3/(5 sqrt(2))`
Answer» Correct Answer - D

Discussion

140.	Evaluate : `(i) int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))` `(ii) (dx)/((1+x+x^(2)))`A. `log ((1+sqrt(3))/(5+ 3sqrt(3)))`B. `log ((5+ 3sqrt(3))/(1+sqrt(3)))`C. `log ((1+sqrt(3))/(5+ sqrt(3)))`D. `log ((5+ sqrt(3))/(1+sqrt(3)))`
Answer» Correct Answer - B

Discussion

141.	`int_(0)^(2)(dx)/(sqrt(4-x^(2))=?`A. `pi / 2`B. `(3pi ) / 2`C. `pi`D. `3pi`
Answer» Correct Answer - C

Discussion

142.	`int_(0)^(2)(dx)/(sqrt(4-x^(2))=?`A. `pi / 2`B. `(3pi ) / 2`C. `pi`D. 0
Answer» Correct Answer - A

Discussion

143.	`int_0^1sin^(- 1)((2x)/(1+x^2))dx`A. `pi/2+ 2log 2 `B. `pi/2- 2log 2 `C. `pi/2+log 2 `D. `pi/2-log 2 `
Answer» Correct Answer - D

Discussion

144.	The correct evalution of `int_(0)^(pi//2) sin x sin 2x dx ` isA. `4/3`B. `1/3`C. `3/4`D. `2/3`
Answer» Correct Answer - D

Discussion

145.	`int_(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))dx`A. `sqrt(2)pi`B. `2pi`C. `pi/sqrt(2)`D. `pi/2`
Answer» Correct Answer - A

Discussion

146.	`int _(0) ^(1//2) dx/((1-2x^(2))sqrt(1-x^(2)))=`A. `(-1)/2 log (2+sqrt(3))`B. `(1)/2 log (2+sqrt(3))`C. `(-1)/4 log (2+sqrt(3))`D. `(1)/4 log (2+sqrt(3))`
Answer» Correct Answer - B

Discussion

147.	`int_(4)^(2) (x^(2) +x)/sqrt(2x+1)dx= `A. `228 / 5 - sqrt(5)`B. `228/5 + sqrt(5)`C. `57 / 5 - sqrt(5)`D. `57/5 sqrt(5)`
Answer» Correct Answer - C

Discussion

148.	`int_(0)^(pi//2) e^(x^(2))/(e^(x^(2)+ e^((pi/2-x)^(2))))dx=`A. `pi/4`B. `pi/2`C. `pi^(2)/e^(16) `D. `pi^(2)/e^(4) `
Answer» Correct Answer - A

Discussion

149.	If `int_1^a (3x^2 + 2x +1)dx = 11` then the value of `a` isA. `-4`B. 4C. `-2`D. 2
Answer» Correct Answer - D

Discussion

150.	`int_(0) ^( pi//2) (root(n)(secx))/(root(n) (secx )+ root (n) ("cosec "x)) dx=`A. `pi/2`B. `pi/3`C. `pi/4`D. `pi/6`
Answer» Correct Answer - C

Discussion

Explore topic-wise InterviewSolutions in .

If `int_(a)^(b)f(x)dx=int_(a)^(b)phi(x)dx`, then-A. `f(x)=phi(x)`B. `f(x)-phi(x)=c`C. `f(x)+phi(x)=c`D. none of these

The value of `int_(0)^(pi)sinthetad theta` is-

`int_(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x + cos^(4)x)dx=`A. `pi/2`B. `pi/4`C. `(3pi)/2`D. `(3pi)/4`

`int_(-pi//2)^(pi//2)sin^(2)xdx`A. `pi/2`B. `pi/4`C. `pi/2-1/4`D. `pi/4-1/2`

If `altcltb` then `int_(a)^(b)f(x)dx` is equal to-A. `int_(a)^(c)f(x)dx+int_(b)^(c)f(x)dx`B. `int_(a)^(c)f(x)dx-int_(c)^(b)f(x)dx`C. `int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx`D. `int_(c)^(a)f(x)dx-int_(b)^(c)f(x)dx`

`int_(0)^(na)f(x)dx=nint_(0)^(a)f(x)dx` if-A. `f(a-x)=f(x)`B. `f(n+x)=f(x)`C. `f(n-x)=f(x)`D. `f(a+x)=f(x)`

If `f(2a-x)=-f(x)` then `int_(0)^(2a)f(x)dx` is equal to-A. `int_(0)^(a)f(x)dx`B. 0C. `int_(-a)^(a)f(x)dx`D. 1

`int_(-(pi)/(2))^((pi)/(2))cosxdx`A. 2B. 1C. 0D. `(1)/(2)`

`lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))}` is equal to-A. `(pi)/(2)`B. `sin^(-1)(1)`C. `cos^(-1)0`D. `2tan^(-1)(1)`

`int_(pi//3)^(pi//2) dx/(sinx+ sin 2x)=`A. `2/3 log 2- 1/2 log 3`B. `4/3 log 2 - 1/2 log 3 `C. `2/3 log 2 - 3/2 log 3 `D. `4/3log 2- 3/2log 3`

`int_(0)^(pi//2) (cosx)/((1+sin x)(2+sin x) ) dx = `A. `log (2/3)`B. `log(3/2)`C. `log(4/3)`D. `log(3/4)`

`int_(0)^(pi//2) (1+ 2 cos x)/((2+ cosx )^(2) )dx = `A. `pi`B. `2`C. `pi/2`D. `1/2`

`int_(0)^(pi//2) (cosx)/((4+sin x)(3+sin x) ) dx = `A. `log (16/15)`B. `log(15/16)`C. `log (4/15)`D. `log(15/4)`

`int_(pi//4) ^(3pi//4) dx/((sin x - 2 cosx)(2sin x + cos x))=`A. `1/5 log 3`B. `1/5 log 9`C. `5 log 3`D. `5 log 9`

`int_(0)^(pi//2) sin ^(3) x cos^(3) x" "dx = `A. `1/12`B. `1/24`C. `1/3`D. `1/6`

`int_(2)^(3)x^(2)dx`A. `211/5`B. `(-211)/5`C. 55D. -55

Let `f(x)=sin^(4)x-cos^(4)xandg(x)=1-2sin^(2)xcos^(2)x`. `intg(x)dx`=A. `(3x)/(4)-(cos4x)/(16)+c`B. `(3x)/(4)+(sin4x)/(16)+c`C. `(3x)/(4)-(sin4x)/(16)+c`D. `(3x)/(4)+(sin4x)/(8)+c`

Which of the following is true ?A. `int_(0)^(1) sqrt(x)" " dx=2/3`B. `int_(0)^(1) sqrt(x)" " dx=(-2)/3`C. `int_(0)^(1) sqrt(x)" " dx=3/2`D. `int_(0)^(1) sqrt(x)" " dx=(-3)/2`

`int_(0)^(pi//2) sin ^(2) x cos^(3) x" "dx = `A. `pi`B. 0C. `pi/2`D. `pi/4`

Evaluate the following : `int_(0)^(1)(1-x^(2))/(1+x^(2))dx`A. `pi/2 - 1`B. `pi/2+ 1`C. `pi/4 -1`D. `pi/4 +1`

`int_(4)^(9) dx/sqrt(x) =`A. 1B. -2C. 2D. -1

`int_(4)^(7)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=`A. `(-11) / 2`B. `11/ 2`C. `(-3)/2`D. `3/2`

`int_(0)^(1//sqrt(2))(sin^(-1)x)/((1-x^(2))^(3//2))dx=?`A. `pi/4+1/2log2`B. `pi/4-1/2log2`C. `pi/2+1/4log2`D. `pi/2-1/4log2`

Evaluate the following : `int_(0)^(1)(x^(2)-2)/(x^(2)+1)dx`A. `1+pi/4`B. `1-pi/4`C. `1+(3pi)/4`D. `1-(3pi)/4`

Prove that `int_(a)^(b)(f(x))/(f(x)+f(a+b-x)) dx=(b-a)/(2)`.A. `(b-a)/2`B. `(b-a)/4`C. `(b+a)/2`D. `(b+a) /4`

`int_(2)^(7) sqrt(x)/ (sqrt(x) + sqrt(9-x))dx=`A. `9/2`B. `(-9)/2`C. `5/2`D. `(-5)/2`

`int_(0)^(1) (x^(2) + 3x+2)/sqrt(x) dx=`A. `8/5`B. `16/5`C. `32/5`D. `64/5`

`If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx.` thenA. `I = J`B. `IltJ`C. `IgtJ`D. `I+J=pi/4`

`int_(-pi) ^(pi) (sin^(4) x) / (sin ^(4) x + cos^(4)x)dx=`A. `pi`B. `2pi`C. `pi/2`D. `(3pi)/2`

`int_(1)^(2) sqrt(x)/ (sqrt(3-x) + sqrt(x))dx=`A. `(-1)/2`B. `1/2`C. `3/2`D. `(-3)/2`

`int_(0)^(1) (dx)/(sqrt(1+x)sqrt(x))=`A. `2/3 (sqrt(2)-1)`B. `2/3(sqrt(2)+1)`C. `4/3(sqrt(2)-1)`D. `4/3(sqrt(2)+1)`

`int_(0)^(1) x^(2)/(x^(2)+1)dx=`A. `2 - pi /4`B. `2 + pi/4`C. `1-pi/4`D. `1+pi/4`

`int_(0)^(pi//2)cos^(2) x" "dx=`A. `(3pi)/4`B. `pi/4`C. `(3pi)/2`D. `pi/2`

Evaluate the following : `int_(0)^(1)(1)/(sqrt(3+2x-x^(2)))dx`A. `pi/4`B. `pi/2`C. `pi/6`D. `pi/12`

Evaluate: `int_0^2(5x+1)/(x^2+4)dx`A. `5/2 log 2 - pi/4`B. `5/2 log 2 +pi/4`C. `5/2 log 2 -pi/8`D. `5/2 log 2 +pi/8`

`int_(3)^(5) (dx)/(sqrt(x+4)+sqrt(x-2))=`A. `1/9 (28-3sqrt(3) - 7 sqrt(7))`B. `1/9 (28-3sqrt(3) + 7 sqrt(7))`C. `1/9 (28+3sqrt(3) -7 sqrt(7))`D. `1/9 (28+3sqrt(3) +7 sqrt(7))`

Evaluate the following : `int_(1)^(2)(dx)/(x^(2)+6x+5)`A. `1/4 log (9/7)`B. `1/4 log (7/9)`C. `1/2 log (3/7)`D. `1/2 log (7/3)`

`int_0^a(dx)/(sqrt(a x-x^2))`A. `pi/2`B. `pi/4`C. `pi`D. 0

Evaluate the following : `int_(0)^(pi//4)sin 3x sin 2x dx`A. `(3sqrt(2))/5`B. `(2sqrt(2))/5`C. `3/(10 sqrt(2))`D. `3/(5 sqrt(2))`

Evaluate : `(i) int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))` `(ii) (dx)/((1+x+x^(2)))`A. `log ((1+sqrt(3))/(5+ 3sqrt(3)))`B. `log ((5+ 3sqrt(3))/(1+sqrt(3)))`C. `log ((1+sqrt(3))/(5+ sqrt(3)))`D. `log ((5+ sqrt(3))/(1+sqrt(3)))`

`int_(0)^(2)(dx)/(sqrt(4-x^(2))=?`A. `pi / 2`B. `(3pi ) / 2`C. `pi`D. `3pi`

`int_(0)^(2)(dx)/(sqrt(4-x^(2))=?`A. `pi / 2`B. `(3pi ) / 2`C. `pi`D. 0

`int_0^1sin^(- 1)((2x)/(1+x^2))dx`A. `pi/2+ 2log 2 `B. `pi/2- 2log 2 `C. `pi/2+log 2 `D. `pi/2-log 2 `

The correct evalution of `int_(0)^(pi//2) sin x sin 2x dx ` isA. `4/3`B. `1/3`C. `3/4`D. `2/3`

`int_(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))dx`A. `sqrt(2)pi`B. `2pi`C. `pi/sqrt(2)`D. `pi/2`

`int _(0) ^(1//2) dx/((1-2x^(2))sqrt(1-x^(2)))=`A. `(-1)/2 log (2+sqrt(3))`B. `(1)/2 log (2+sqrt(3))`C. `(-1)/4 log (2+sqrt(3))`D. `(1)/4 log (2+sqrt(3))`

`int_(4)^(2) (x^(2) +x)/sqrt(2x+1)dx= `A. `228 / 5 - sqrt(5)`B. `228/5 + sqrt(5)`C. `57 / 5 - sqrt(5)`D. `57/5 sqrt(5)`

`int_(0)^(pi//2) e^(x^(2))/(e^(x^(2)+ e^((pi/2-x)^(2))))dx=`A. `pi/4`B. `pi/2`C. `pi^(2)/e^(16) `D. `pi^(2)/e^(4) `

If `int_1^a (3x^2 + 2x +1)dx = 11` then the value of `a` isA. `-4`B. 4C. `-2`D. 2

`int_(0) ^( pi//2) (root(n)(secx))/(root(n) (secx )+ root (n) ("cosec "x)) dx=`A. `pi/2`B. `pi/3`C. `pi/4`D. `pi/6`