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The area bounded by the graph of y=f(x),...

The area bounded by the graph of `y=f(x), f(x) gt0` on [0,a] and x-axis is `(a^(2))/(2)+(a)/(2) sin a +(pi)/(2) cos a ` then find the value of `f((pi)/(2))`.

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3)`
According to the equestion `overset(a)underset(0)intf(x)dx=(a^(2))/(2)+(a)/(2)sin a +(pi)/(2) cos a `
`therefore" "f(a)=(d)/(da)((a^(2))/(2)+(a)/(2)sin a +(pi)/(2)cos a)`
`a+(a)/(2) cos a +(1)/(2)sin a -(pi)/(2) sin a`
`therefore" "f((pi)/(2))=(1)/(2)`
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