The Fourier Cosine Integral of a Function F Defined On [

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) $2 \int _ { 0 } ^ { \infty } \left[ \int _ { 0 } ^ { \infty } f ( x ) \cos ( \alpha x ) d \alpha \right] \cos ( \alpha x ) d x / \pi$

Correct Answer:

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