207 + Interview Questions in INTEGRATION-DEFINITE-INTEGRALS IN GENERAL AWARENESS

1.	`int_(pi//4)^(pi//3)(sec x)/(sin x)dx =`A. log 9B. `log(sqrt(3))`C. log 3D. log 8
Answer» Correct Answer - B

Discussion

2.	`int_(0)^(log 2)(e^(x))/(1+e^(x))dx=`A. log 6B. `log((2)/(3))`C. `log((3)/(2))`D. log 8
Answer» Correct Answer - C

Discussion

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

Discussion

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

Discussion

5.	`int_(1//pi)^(2//pi)(sin(1//x))/(x^(2))dx=?`A. `(1)/(pi)`B. `(2)/(pi)`C. `(3)/(pi)`D. 1
Answer» Correct Answer - D

Discussion

6.	`int_(1)^(e )((log x)^(3))/(x)dx=`A. `e^(4)`B. `(1)/(4)`C. `(1)/(4)(e^(4)-1)`D. 0
Answer» Correct Answer - B

Discussion

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

Discussion

8.	`int_(0)^(1)(tan^(-1)x)/((1+x^(2)))dx`A. `(pi)/(2)`B. `(pi)/(16)`C. `(pi^(2))/(32)`D. `(pi)/(8)`
Answer» Correct Answer - C

Discussion

9.	`int_(-1)^(1)(1)/(a^(2)e^(x)+b^(2)e^(-x))dx=`A. `(1)/(ab)log(a^(2)e^(2)+b^(2))`B. `(1)/(ab)log(a^(2)+b^(2)e^(2))`C. `(1)/(ab)[tan^(-1)((ae )/(b))-tan^(-1)((a)/(be))]`D. `(1)/(Ab)tan^(-1)[(ab(e^(2)-1))/(e^(2)+1)]`
Answer» Correct Answer - C

Discussion

10.	`int_(2)^(3)(1)/(x(x^(3)-1))dx=`A. `(1)/(3)log((208)/(189))`B. `(1)/(3)log((26)/(7))`C. `(1)/(3)log((7)/(26))`D. `log((3)/(2))`
Answer» Correct Answer - A

Discussion

11.	`int_(0)^(1)x^(3)sqrt(1-x^(2))dx=`A. `(1)/(15)`B. `(22)/(15)`C. `(4)/(15)`D. `(2)/(15)`
Answer» Correct Answer - D

Discussion

12.	`int_(0)^(1)x^(2)sqrt(1-x^(2))dx=`A. 1B. `(1)/(2)`C. `(pi)/(16)`D. `(1)/(15)`
Answer» Correct Answer - C

Discussion

13.	The value of `int0 1tan^(-1)((2x-1)/(1+x-x^2))dx`is(A) 1 (B) 0 (C) -1 (D)`pi/4`
Answer» Correct Answer - A

Discussion

14.	`int_(0)^(pi)(1)/(41+40 cos x)dx=`A. `(pi)/(3)`B. `(pi)/(2)`C. `(pi)/(9)`D. `(pi)/(12)`
Answer» Correct Answer - C

Discussion

15.	`int_(0)^(1)(x^(2)+3x+2)/(sqrt(x))dx=`A. `(23)/(5)`B. `(32)/(5)`C. `-(32)/(5)`D. `(5)/(32)`
Answer» Correct Answer - B

Discussion

16.	`int_(0)^(2)(3x^(2)+2x-1)dx=`A. 7B. 8C. 9D. 10
Answer» Correct Answer - D

Discussion

17.	`int_(0)^(1)2^(x)dx=`A. log 2B. `log_(2)e`C. `(1)/(log_(2)e)`D. 1
Answer» Correct Answer - B

Discussion

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

Discussion

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

Discussion

20.	`int_(1)^(9)sqrt(x)dx =`A. `(25)/(3)`B. `(522)/(3)`C. `(255)/(3)`D. `(52)/(3)`
Answer» Correct Answer - D

Discussion

21.	`int_(4)^(9)(x-1)/(1+sqrt(x))dx=`A. `-(23)/(3)`B. `-(32)/(3)`C. `(23)/(3)`D. `(32)/(3)`
Answer» Correct Answer - C

Discussion

22.	`int_(0)^(1)(1)/(sqrt(x+3)+sqrt(x+2))dx=`A. `(4)/(3)(sqrt(2)-3sqrt(3)+4)`B. `(2)/(3)(8-6sqrt(3))`C. `2+sqrt(3)`D. `(4)/(3)(sqrt(2)+3sqrt(3)-4)`
Answer» Correct Answer - A

Discussion

23.	` int_(0)^(pi//2) sin 2x log (tan x)` dx is equal to
Answer» Correct Answer - A

Discussion

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

Discussion

25.	If `f(a-x)=f(x)` and `int_(0)^(a//2)f(x)dx=p`, then : `int_(0)^(a)f(x)dx=`
Answer» Correct Answer - C

Discussion

26.	Evaluate : `(i) int_(0)^(1)x(1-x)^(n)dx` `(ii) int_(0)^(1)x(1-x)^(3//2)dx`A. 1B. 0C. `(4)/(35)`D. `(35)/(4)`
Answer» Correct Answer - C

Discussion

27.	`int_(-pi)^(pi)(1-x^(2))sin x cos^(2)x dx=`
Answer» Correct Answer - A

Discussion

28.	Evaluate:`int_(-1/2)^(1/2)cosxlog(1-x)/(1+x)dx`A. `-(1)/(2)`B. `(1)/(2)`C. 2D. 0
Answer» Correct Answer - D

Discussion

29.	`int_(2)^(3)(x)/((x+2)(x+3))dx=`A. `log((6^(3).4^(2))/(5^(5)))`B. `log((3^(6).2^(4))/(5^(5)))`C. `log((24)/(5))`D. `log((4^(2).5^(3))/(6^(4)))`
Answer» Correct Answer - A

Discussion

30.	`int_(2)^(3)(1)/(2x^(2)+3x-2)dx=`A. `(1)/(5)tan^(-1)((4)/(3))`B. `(1)/(5)log((4)/(3))`C. `5 tan^(-1)((3)/(4))`D. `5 log ((3)/(4))`
Answer» Correct Answer - B

Discussion

31.	`int_(2)^(3)(1)/(x^(2)+5x+6)dx =`A. `tan^(-1)((25)/(24))`B. `log((25)/(24))`C. `sin^(-1)((25)/(24))`D. `sec^(-1)((25)/(24))`
Answer» Correct Answer - B

Discussion

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

Discussion

33.	The integral `underset(0)overset(a)int (g(x))/(f(x)+f(a-x))dx` vanishes, ifA. g(x) is an odd functionB. `f(x)=f(a-x)`C. `g(x)=-g(a-x)`D. `f(a-x)=g(x)`
Answer» Correct Answer - C

Discussion

34.	`int_(1)^(2)(1)/(x sqrt(x^(2)-1))dx=`A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(4)`D. `(pi)/(6)`
Answer» Correct Answer - B

Discussion

35.	`int_(0)^(1)((cot^(-1)x)^(2))/(1+x^(2))dx=`A. `(pi^(3))/(8)`B. `(pi^(3))/(64)`C. `(7pi^(3))/(192)`D. `(pi^(3))/(192)`
Answer» Correct Answer - C

Discussion

36.	`int_(sqrt(3))^(sqrt(8))xsqrt(1+x^(2))dx=?`A. 224B. 324C. 432D. 234
Answer» Correct Answer - D

Discussion

37.	`int_0^1 x^5/(1+x^12) dx`A. `(pi)/(12)`B. `(pi)/(6)`C. `(pi)/(4)`D. `(pi)/(3)`
Answer» Correct Answer - A

Discussion

38.	`int_(0)^(1)(x^(4))/(1+x^(10))dx=`A. `(pi)/(5)`B. `(pi)/(10)`C. `(pi)/(20)`D. `(pi)/(25)`
Answer» Correct Answer - C

Discussion

39.	`int_(0)^(pi//2)(1)/(2-sin x)dx=`A. `(pi)/(4)`B. `(pi)/(2)`C. `(2pi)/(3sqrt(3))`D. `(5pi)/(4)`
Answer» Correct Answer - C

Discussion

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

Discussion

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

Discussion

42.	`int_(0)^(pi//2)(x)/(tan x)dx=`A. `(pi)/(2)log 2`B. log 2C. `pi log 3`D. `pi log 4`
Answer» Correct Answer - A

Discussion

43.	`int_(1//2)^(1)(1)/(4x^(2)-4x+10)dx=`A. `tan^(-1)((1)/(3))`B. `(1)/(6)tan^(-1)((1)/(3))`C. `(1)/(8)tan^(-1)((1)/(3))`D. `-(1)/(6)log 3`
Answer» Correct Answer - B

Discussion

44.	`int_(1)^(2)(1)/(x^(2)-4x+7)dx=`
Answer» Correct Answer - D

Discussion

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

Discussion

46.	`int_(0)^(pi)sin 5 x cos 4x dx=`A. `(5)/(9)`B. `(9)/(5)`C. `(10)/(9)`D. `(10)/(3)`
Answer» Correct Answer - C

Discussion

47.	`int_(0)^(pi//4)(sin^(9)x)/(cos^(11)x)dx=`A. `(pi)/(4)`B. `(1)/(10)`C. `-(1)/(10)`D. 0
Answer» Correct Answer - B

Discussion

48.	If n is an integer, then `int_(0)^(pi)(sin 2nx)/(sin x)dx=`A. `(pi)/(4)`B. 0C. `(pi)/(2)`D. `(pi)/(8)`
Answer» Correct Answer - B

Discussion

49.	`int_-1^1[cos^-1x] dx` (where [.] denotes greatest integer function)A. `(pi)/(3)`B. `(pi)/(2)`C. `pi`D. `(3pi)/(2)`
Answer» Correct Answer - C

Discussion

50.	`int_(-pi//2)^(pi//2) x sin x cos x dx=`
Answer» Correct Answer - C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

`int_(pi//4)^(pi//3)(sec x)/(sin x)dx =`A. log 9B. `log(sqrt(3))`C. log 3D. log 8

`int_(0)^(log 2)(e^(x))/(1+e^(x))dx=`A. log 6B. `log((2)/(3))`C. `log((3)/(2))`D. log 8

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

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

`int_(1//pi)^(2//pi)(sin(1//x))/(x^(2))dx=?`A. `(1)/(pi)`B. `(2)/(pi)`C. `(3)/(pi)`D. 1

`int_(1)^(e )((log x)^(3))/(x)dx=`A. `e^(4)`B. `(1)/(4)`C. `(1)/(4)(e^(4)-1)`D. 0

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

`int_(0)^(1)(tan^(-1)x)/((1+x^(2)))dx`A. `(pi)/(2)`B. `(pi)/(16)`C. `(pi^(2))/(32)`D. `(pi)/(8)`

`int_(-1)^(1)(1)/(a^(2)e^(x)+b^(2)e^(-x))dx=`A. `(1)/(ab)log(a^(2)e^(2)+b^(2))`B. `(1)/(ab)log(a^(2)+b^(2)e^(2))`C. `(1)/(ab)[tan^(-1)((ae )/(b))-tan^(-1)((a)/(be))]`D. `(1)/(Ab)tan^(-1)[(ab(e^(2)-1))/(e^(2)+1)]`

`int_(2)^(3)(1)/(x(x^(3)-1))dx=`A. `(1)/(3)log((208)/(189))`B. `(1)/(3)log((26)/(7))`C. `(1)/(3)log((7)/(26))`D. `log((3)/(2))`

`int_(0)^(1)x^(3)sqrt(1-x^(2))dx=`A. `(1)/(15)`B. `(22)/(15)`C. `(4)/(15)`D. `(2)/(15)`

`int_(0)^(1)x^(2)sqrt(1-x^(2))dx=`A. 1B. `(1)/(2)`C. `(pi)/(16)`D. `(1)/(15)`

The value of `int0 1tan^(-1)((2x-1)/(1+x-x^2))dx`is(A) 1 (B) 0 (C) -1 (D)`pi/4`

`int_(0)^(pi)(1)/(41+40 cos x)dx=`A. `(pi)/(3)`B. `(pi)/(2)`C. `(pi)/(9)`D. `(pi)/(12)`

`int_(0)^(1)(x^(2)+3x+2)/(sqrt(x))dx=`A. `(23)/(5)`B. `(32)/(5)`C. `-(32)/(5)`D. `(5)/(32)`

`int_(0)^(2)(3x^(2)+2x-1)dx=`A. 7B. 8C. 9D. 10

`int_(0)^(1)2^(x)dx=`A. log 2B. `log_(2)e`C. `(1)/(log_(2)e)`D. 1

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

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

`int_(1)^(9)sqrt(x)dx =`A. `(25)/(3)`B. `(522)/(3)`C. `(255)/(3)`D. `(52)/(3)`

`int_(4)^(9)(x-1)/(1+sqrt(x))dx=`A. `-(23)/(3)`B. `-(32)/(3)`C. `(23)/(3)`D. `(32)/(3)`

`int_(0)^(1)(1)/(sqrt(x+3)+sqrt(x+2))dx=`A. `(4)/(3)(sqrt(2)-3sqrt(3)+4)`B. `(2)/(3)(8-6sqrt(3))`C. `2+sqrt(3)`D. `(4)/(3)(sqrt(2)+3sqrt(3)-4)`

` int_(0)^(pi//2) sin 2x log (tan x)` dx is equal to

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

If `f(a-x)=f(x)` and `int_(0)^(a//2)f(x)dx=p`, then : `int_(0)^(a)f(x)dx=`

Evaluate : `(i) int_(0)^(1)x(1-x)^(n)dx` `(ii) int_(0)^(1)x(1-x)^(3//2)dx`A. 1B. 0C. `(4)/(35)`D. `(35)/(4)`

`int_(-pi)^(pi)(1-x^(2))sin x cos^(2)x dx=`

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

`int_(2)^(3)(x)/((x+2)(x+3))dx=`A. `log((6^(3).4^(2))/(5^(5)))`B. `log((3^(6).2^(4))/(5^(5)))`C. `log((24)/(5))`D. `log((4^(2).5^(3))/(6^(4)))`

`int_(2)^(3)(1)/(2x^(2)+3x-2)dx=`A. `(1)/(5)tan^(-1)((4)/(3))`B. `(1)/(5)log((4)/(3))`C. `5 tan^(-1)((3)/(4))`D. `5 log ((3)/(4))`

`int_(2)^(3)(1)/(x^(2)+5x+6)dx =`A. `tan^(-1)((25)/(24))`B. `log((25)/(24))`C. `sin^(-1)((25)/(24))`D. `sec^(-1)((25)/(24))`

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

The integral `underset(0)overset(a)int (g(x))/(f(x)+f(a-x))dx` vanishes, ifA. g(x) is an odd functionB. `f(x)=f(a-x)`C. `g(x)=-g(a-x)`D. `f(a-x)=g(x)`

`int_(1)^(2)(1)/(x sqrt(x^(2)-1))dx=`A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(4)`D. `(pi)/(6)`

`int_(0)^(1)((cot^(-1)x)^(2))/(1+x^(2))dx=`A. `(pi^(3))/(8)`B. `(pi^(3))/(64)`C. `(7pi^(3))/(192)`D. `(pi^(3))/(192)`

`int_(sqrt(3))^(sqrt(8))xsqrt(1+x^(2))dx=?`A. 224B. 324C. 432D. 234

`int_0^1 x^5/(1+x^12) dx`A. `(pi)/(12)`B. `(pi)/(6)`C. `(pi)/(4)`D. `(pi)/(3)`

`int_(0)^(1)(x^(4))/(1+x^(10))dx=`A. `(pi)/(5)`B. `(pi)/(10)`C. `(pi)/(20)`D. `(pi)/(25)`

`int_(0)^(pi//2)(1)/(2-sin x)dx=`A. `(pi)/(4)`B. `(pi)/(2)`C. `(2pi)/(3sqrt(3))`D. `(5pi)/(4)`

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

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

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

`int_(1//2)^(1)(1)/(4x^(2)-4x+10)dx=`A. `tan^(-1)((1)/(3))`B. `(1)/(6)tan^(-1)((1)/(3))`C. `(1)/(8)tan^(-1)((1)/(3))`D. `-(1)/(6)log 3`

`int_(1)^(2)(1)/(x^(2)-4x+7)dx=`

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

`int_(0)^(pi)sin 5 x cos 4x dx=`A. `(5)/(9)`B. `(9)/(5)`C. `(10)/(9)`D. `(10)/(3)`

`int_(0)^(pi//4)(sin^(9)x)/(cos^(11)x)dx=`A. `(pi)/(4)`B. `(1)/(10)`C. `-(1)/(10)`D. 0

If n is an integer, then `int_(0)^(pi)(sin 2nx)/(sin x)dx=`A. `(pi)/(4)`B. 0C. `(pi)/(2)`D. `(pi)/(8)`

`int_-1^1[cos^-1x] dx` (where [.] denotes greatest integer function)A. `(pi)/(3)`B. `(pi)/(2)`C. `pi`D. `(3pi)/(2)`

`int_(-pi//2)^(pi//2) x sin x cos x dx=`