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Question: If for a continuous function f \(\int _ { - a } ^ { a } f ( x ) d x = k \int _ { 0 } ^ { a } ( f ( x...

If for a continuous function f ∫−aaf(x)dx=k∫0a(f(x)+f(−x))\int _ { - a } ^ { a } f ( x ) d x = k \int _ { 0 } ^ { a } ( f ( x ) + f ( - x ) ) dx, then k is

A

0

B

1

C

2

D

–1

Answer

1

Explanation

Solution

use ® ∫−aaf(x)⋅dx=∫0af(x)\int _ { - a } ^ { a } f ( x ) \cdot d x = \int _ { 0 } ^ { a } f ( x ) + f(–x)dx is true for every f(x)

̃ k = 1