For the function on

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

Problem

For the function

f(x)=e^{2x}

[0,1]

, choose the value of

c\in(0,1)

that satisfies

\displaystyle \int_{0}^{1} f(x)\,dx = f(c)\,(1-0)

. (a)

\ln\!\bigl(\dfrac{e^{2}-1}{2}\bigr)

(b)

\dfrac{1}{2}\ln\!\Bigl(\dfrac{e^{2}}{2}\Bigr)

(c)

\dfrac{1}{2}\ln\!\bigl(\dfrac{e^{2}-1}{2}\bigr)

(d)

\dfrac{1}{2}\ln(e^{2}-1)