Prove that _ 0 ^ x _ 0 ^ u f(t) ,dt du = _ 0 ^ x (x - u) f(u) ,du.

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Prove that ∫0x{∫0uf(t) dt}du=∫0x(x−u)f(u) du.\int_{0}^{x} \left\{ \int_{0}^{u} f(t)\,dt \right\} du = \int_{0}^{x} (x - u) f(u)\,du.

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