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Grade:10

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

\int_{0}^{\pi }(f(x)+f''(x))sinxdx = 5
\int_{0}^{\pi }[(f(x)+f''(x))sinx-f'(x)cosx+f'(x)cosx]dx = 5
\int_{0}^{\pi }[f(x)sinx+f''(x)sinx-f'(x)cosx+f'(x)cosx]dx = 5
\int_{0}^{\pi }[-(f'(x)cosx-sinxf(x))+sinxf''(x)+f'(x)cosx]dx = 5
\int_{0}^{\pi }-(cosxf(x))'dx+\int_{0}^{\pi }(sinxf'(x))dx = 5
[-(cosxf(x))]_{0}^{\pi }+(sinxf'(x))_{0}^{\pi } = 5
-(-f(\pi )-f(0)) = 5
f(\pi ) + f(0) = 5
2 + f(0) = 5
f(0) = 3


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