Let and . Define . What is…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

g(x)=x^{2}+1

and

h(x)=x

. Define

A(t)=\displaystyle \int_{0}^{t} \bigl(g(x)-h(x)\bigr)\,dx

. What is

A(2)

? (a)

\dfrac{10}{3}

(b)

\dfrac{4}{3}

(c)

\dfrac{8}{3}

(d)

\dfrac{20}{3}