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Let f(x) be a continuous function such t...

Let f(x) be a continuous function such that the area bounded by the curve `y=f(x),` the x-axis, and the lines `x=0` and `x=a is 1+(a^(2))/(2)sin` a. Then,

A

`((pi)/(2))=1+(pi^(2))/(8)`

B

`f(a)=1+(a^(2))/(2)sina`

C

`f(a)=asina+1/2cosa`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
It is given that `underset(0)overset(a)(int)f(x)dx=1+(a^(2))/(2)sina`
Differentiationg this with respect to a, we get
`f(a)=a sina+(a^(2))/(2)cosa`
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OBJECTIVE RD SHARMA ENGLISH-AREAS OF BOUNDED REGIONS-Chapter Test
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  17. The area between the curve x=-2y^(2)and x=1-3y^(2), is

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