Solveeit Logo
Login

Question

Question: \(\int _ { - 1 } ^ { 1 } x ^ { 17 } \cos ^ { 4 } x d x =\)...

∫−11x17cos⁡4xdx=\int _ { - 1 } ^ { 1 } x ^ { 17 } \cos ^ { 4 } x d x =

A

B

−1- 1

C

0

D

2

Answer

0

Explanation

Solution

Let f(x)=x17cos⁡4xf ( x ) = x ^ { 17 } \cos ^ { 4 } x

f(−x)=(−x)17{cos⁡(−x)}4=−f(x)f ( - x ) = ( - x ) ^ { 17 } \{ \cos ( - x ) \} ^ { 4 } = - f ( x )

Therefore,∫−11x17cos⁡4xdx=0\int _ { - 1 } ^ { 1 } x ^ { 17 } \cos ^ { 4 } x d x = 0.