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Question

If f(x)=x0t sin t dt, then write the value of f(x).


Solution

f(x)=x0tsint dt

Integrate by parts,

f(x)=[t(cost)]x0x01.(cost)dt
f(x)=(x cosx0)+(sint)x0
f(x)=x cosx+sinx

f(x)=x(sinx)cosx+cosx

f(x)=x sin x

Mathematics

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