JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f\left( \pi \right) = 2

and

\int \nolimits_0^\pi \,\,\left[ {f\left( x \right)\,\, + \,\,f''\left( x \right)} \right]\,\,\sin \,\,x\,\,dx = 5,

, then

f\,\,\left( 0 \right)

is equal to, (it is given that

f\left( x \right)

is continuous in

\left[ {0,\,\,\pi } \right]\,

)

View answer and explanation

Correct option: B

Option B (3) is correct because integration by parts is applied to simplify the integral, leading to the equation

f(\pi) + f(0) = 5

, and given

f(\pi) = 2

, we find

f(0) = 3

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