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Integration by Substitution

Question

Let f be a function defined for every x, such that f'' = -f ,f(0)=0, f' (0) = 1, then f(x) is equal to
tanx
$e^{x} - 1$
sinx
2sinx

A

e^{x} - 1

B

sinx

C

tanx

D

2sinx

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Solution

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$\int f^{^{''}} (x) f^{^{'}} (x) = - \int f (x) f^{^{'}} (x)$

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