AP

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Define

P(x)=\displaystyle \int_{0}^{x}\sin(2t^{2}+1)\,dt

. (i) Find

P'(x)

. (ii) Show that

P''(x)=4x\cos(2x^{2}+1)

. (iii) Hence, determine

P''(\sqrt{\pi/2})