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The area bounded between the parabolas x...

The area bounded between the parabolas `x^2=y/4"and"x^2=9y` and the straight line `y""=""2` is (1) `20sqrt(2)` (2) `(10sqrt(2))/3` (3) `(20sqrt(2))/3` (4) `10sqrt(2)`

A

`20 sqrt(2)` sq units

B

`(10sqrt(2))/(3)` sq units

C

`(20sqrt(2))/(3)` sq units

D

`10 sqrt(2)` sq units

Text Solution

Verified by Experts

The correct Answer is:
C

Required area
`=2int_(0)^(2)(3sqrt(y)-(sqrt(y))/(2))dy=2int_(0)^(2)((5)/(2)sqrt(y))dy`
`=5[(y^(3//2))/((3)/(2))]_(y=0)^(y=2)=(10)/(3)(2^(3//2)-0)=(20sqrt(2))/(3)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DEFINITE INTEGRALS -Exercise 2
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  9. The area bounded by the curves y = cos x and y = sin x between the ord...

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  12. For 0 lt= x lt= pi, the area bounded by y = x and y = x + sin x, is

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  13. If the area above the x-axis, bounded by the curves y = 2^(kx) and x =...

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  14. The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^...

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  15. The area in the first quadrant between x^2+y^2=pi^2 and y=sinx is

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  17. The area bounded by y = |sin x|, X-axis and the line |x|=pi is

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  18. Find the area bounded by the x-axis, part of the curve y=(1-8/(x^2)) ,...

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  19. The area bounded by the graph of y=f(x), f(x) gt0 on [0,a] and x-axis ...

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