For let . A previously established relationship shows that for all integers . What is…

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

Problem

For

n\ge 0

let

I_n=\displaystyle\int_{0}^{1}x^{n}e^{x}\,dx

. A previously established relationship shows that

I_n=e-n\,I_{n-1}

for all integers

n\ge 1

. What is the value of

I_4

? (a)

5e-8

(b)

9e-24

(c)

-7e+24

(d)

9e