Let . Which of the following statements about and its derivative is…

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

Problem

Let

F(x)=\displaystyle \int_{0}^{x} t^{2} e^{-t^{2}}\,dt

. Which of the following statements about

F

and its derivative is true? (a)

F

can be expressed using elementary functions, but

F'(x)

cannot. (b) Neither

F

nor

F'(x)

can be expressed using elementary functions. (c)

F

cannot be expressed using elementary functions, but

F'(x)

can. (d) Both

F

and

F'(x)

can be expressed using elementary functions.