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Question: n, <img src="https://cdn.pureessence.tech/canvas_44.png?top_left_x=904&top_left_y=1462&width=300&hei...

n, dx =

A

–1

B

0

C

1

D

p

Answer

0

Explanation

Solution

I = ∫0πesin⁡2xcos⁡3(2n+1)xdx\int _ { 0 } ^ { \pi } e ^ { \sin ^ { 2 } x } \cos ^ { 3 } ( 2 n + 1 ) x d x

= ∫0πesin⁡2x(π−x)\int _ { 0 } ^ { \pi } e ^ { \sin ^ { 2 } x ( \pi - x ) } cos3 {(2n + 1) (p – x)} dx

= ∫0πesin⁡2x{cos⁡3(2n+1)}(π−x)dx\int _ { 0 } ^ { \pi } \mathrm { e } ^ { \sin ^ { 2 } x } \left\{ \cos ^ { 3 } ( 2 \mathrm { n } + 1 ) \right\} ( \pi - x ) \mathrm { dx }

= –

= – I 2 I = 0 ̃ I = 0