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How do you evaluate the integral of #intx sin(5x) dx#?

Answer 1

Christopher Agresta

If you set #u=5x# then #x=1/5u# and #du=5dx# so we have that

#int x*sin(5x)dx= 1/5 int u*sinu du=1/25*(sin(5x)-5x*cos(5x))+c#

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Answer 2

Isaiah Allen

To evaluate the integral ∫x sin(5x) dx, you can use integration by parts. Let u = x and dv = sin(5x) dx. Then, differentiate u to get du and integrate dv to get v. After that, apply the integration by parts formula:

∫u dv = uv - ∫v du

Substitute the values of u, v, du, and dv into the formula and integrate accordingly. This will give you the result of the integral.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.