The Fourier cosine integral of a function f defined on $[ 0 , \infty ]$ is
A) $2 \int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d x \right] \cos ( \alpha x ) d \alpha / \pi$
B) $\int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d x \right] \cos ( \alpha x ) d \alpha / \pi$
C) $2 \int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d x \right] \cos ( \alpha x ) d \alpha$
D) $\int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d \alpha \right] \cos ( \alpha x ) d x$
E) $2 \int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d \alpha \right] \cos ( \alpha x ) d x / \pi$

Question

Quizplus · Accepted Answer

The Fourier cosine integral of a function f defined on $[ 0 , \infty ]$ is given by:$F ( \alpha ) = \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d x$Therefore, the Fourier cosine integral of a function f defined on $[ 0 , \infty ]$ is:$2 \int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d x \right] \cos ( \alpha x ) d \alpha / \pi$

The Fourier Cosine Integral of a Function F Defined On [