If a curve `y=asqrtx+bx` passes through the point (1,2) and the area b – InterviewSolution

InterviewSolution

1.	If a curve `y=asqrtx+bx` passes through the point (1,2) and the area bounded by the curve, line x=4 and x-axis is 8 square units, thenA. `a=3,b=-1`B. `a=3,b=1`C. `a=-3,b=1`D. `a=-3,b=-1`
Answer» Correct Answer - a It is given that `y=asqrtx+bx` passes through the point (1,2). `therefore2=a+b" "...(i)` It is given that `underset(0)overset(4)(int)(asqrtx+bx)dx=8` `implies[(2)/(3)ax^(3//2)+b/2x^(2)]_(0)^(4)=8` `implies16/3a+8b=8implies2/3a+b=1" "...(ii)` Solving (i)and (ii), we get `a=3, b=-1.`

Discussion

No Comment Found

Related InterviewSolutions

Let `A_n`be the area bounded by the curve `y=(tanx)^n`and the lines `x=0,y=0,`and `x=pi/4dot`Prove that for `n >2,A_n+A_(n-2)=1/(n-1)`and deduce `1/(2n+2)A. `A_(n)+A_(n-2)=(1)/(n-1)`B. `A_(n)+A_(n-2) lt (1)/(n-1)`C. `A_(n)-A_(n-2)=(1)/(n-1)`D. none of these
The area bounded by `y=x^(2)+1` oand the tangents to it drawn from the origin, isA. `8//2` sq. unitsB. `1//3` sq. unitsC. `2//3` sq. unitsD. none of these
The area enclosed by the curves`y= sinx+cosx and y = | cosx-sin x |` over the interval `[0,pi/2]`A. `4(sqrt(2)-1)`B. `2sqrt(2)(sqrt(2)-1)`C. `2(sqrt(2)+1)`D. `2sqrt(2)(sqrt(2)+1)`
The area (in square units), bounded by `y=2-x^(2)` and `x+y=0` , isA. `(7)/(2)` sq. unitsB. `(9)/(2)` sq. unitsC. 9 sq. unitsD. none of these
The area (in square units) bounded by the curve `y^(2)=8xand x^(2)=8y,` isA. `16/3`B. `3/16`C. `14/3`D. `3/14`
The area of the figure bounded by `|y|=1-x^(2)` is in square units,A. `4//3`B. `8//3`C. `16//3`D. `5//3`
The area (in square units) of the closed figure bounded by `x=-1,x=2and y={{:(-x^(2)+2","x le1),(2x-1","xgt1):}` and the abscissa axis, isA. `16//3`B. `13//3`C. `13//3`D. `7//3`
Find the area bounded by the parabola `y=x^2+1`and the straight line `x+y=3.`A. `(45)/(7)`B. `(3)/(2)`C. `(32)/(3)`D. `(3)/(32)`
Examples: Find the area bounded by the parabola `y^2 = 4ax` and its latus rectum.
Area bounded by the parabola `y^2=x` and the line `2y=x` is (A) `4/3` (B) `1` (C) `2/3` (D) `1/3`A. `4//3`B. 1C. `2//3`D. `1//3`