Let where g(t)= cases t^ 2 , & t< -1

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

Problem

Let

G(x)=\displaystyle\int_{-10}^{x} g(t)\,dt

where

g(t)=\begin{cases} t^{2}, & t< -1,\\ \sin t, & t\ge -1. \end{cases}

State all real numbers at which

G

is differentiable and give a formula for

G'(x)

where it exists.