Let the accumulation function be defined by F(x)= _ x ^ x^2+1 (t^3+2t) ,dt

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

Problem

Let the accumulation function

F

be defined by

F(x)=\int_{x}^{x^2+1} (t^3+2t)\,dt,

where

x

is any real number for which the integral is well defined. (a) Determine

F'(x)

for all real

x

. Show all work leading to your result. (b) Evaluate

F'(1)

and interpret the meaning of this value in the context of the accumulation function

F