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Grade 10Integral Calculus

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7

3

5

1

Question image for options 7 3 5 1

Aditya Kartikeya

12 Years agoGrade 10

1 Answer

Jitender Singh

12 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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