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If f^(prime)(x)=asinx+bcosx and f^(prime...

If `f^(prime)(x)=asinx+bcosx` and `f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=5` , find `f(x)` .

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`f'(x)=asinx+bcosx`

Given that, `f'(0)=4`

`b=4`

`intf'(x)\dx=-acosx+bsinx+C`

`f(x)=-acosx+4sinx+C`

`f(0)=3`

`-a+C=3`

`f(pi/2)=5`

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