Consider the function defined on the interval whose derivative is g'(x)=e^ 2x -3

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

Problem

Consider the function

g

defined on the interval

[0,4]

whose derivative is

g'(x)=e^{2x}-3.

It is known that

g(0)=4

. (a) Find an explicit formula for

g(x)

0\le x\le 4

. (b) Evaluate

g(2)

. (c) Compute

\displaystyle\int_{0}^{2} g'(x)\,dx

and compare the result with

g(2)-g(0)

. State the theorem that supports your comparison and explain its significance in this context.