Suppose and are two continuous functions defined for

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

Problem

Suppose

f(x)

and

g(x)

are two continuous functions defined for

0\le x\le1

. Given

f(x)=\int_{0}^{1}e^{x+t}f(t)\,dt

and

g(x)=\int_{0}^{1}e^{x+t}g(t)\,dt+x

, find the value of

g(0)-f(0)

. (1)

\frac{2}{3-e^2}

(2)

\frac{3}{e^2-2}

(3)

\frac{1}{e^2-1}

(4)

0