# Integration help plz I need help proving this integral [duplicate]

This question is an exact duplicate of:

We are asked to prove the following integral;

$$\int_0^x(\int_0^tf(u)du)dt=\int_0^xf(u)(x-u)dx$$

We have to use integration by parts and then by this apply the fundamental theorem of calculus which I believe need to be applied to the derivative part of the one done by parts. I haven't seen anything like this before.

Any help would be greatly appreciated

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This question was marked as an exact duplicate of an existing question.

Your region is bound by $$u=t$$, $$u = 0$$, and $$t = x$$
$$\int_0^x\int_u^x f(u)\, dt\, du$$
And integrate with respect to $$t$$.