For , let . Define the function…

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

Problem

For

x \ge 0

, let

f(t)=\ln\bigl(t^{2}+1\bigr)

. Define the function

g(x)=\int_{0}^{x^{2}} f(t)\,dt

. (a) Find a simplified expression for

g'(x)

. (b) Evaluate

g'(3)

. (c) Write the equation of the line tangent to the graph of

y=g(x)

x=3