Define p(x)= _ 0 ^ x 1+t^ 3 ,dt ; + ; _ x ^ x 1+t^ 3 ,dt

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

Problem

Define p(x)=∫0sin⁡x1+t3 dt  +  ∫sin⁡xx1+t3 dt.p(x)=\int_{0}^{\sin x} \sqrt{1+t^{3}}\,dt\; +\; \int_{\sin x}^{x} \sqrt{1+t^{3}}\,dt. Determine p′(x)p'(x) for all real xx.

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