Let on the interval

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

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

on the interval

[0,2]

. If

c\in(0,2)

satisfies

\displaystyle \int_{0}^{2} f(x)\,dx = f(c)(2-0)

, then

c

equals (a)

\sqrt{\dfrac{11}{3}}

(b)

\sqrt{\dfrac{7}{3}}

(c)

\dfrac{2}{\sqrt{3}}

(d)

\dfrac{\sqrt{3}}{2}