How does ∫ π / 3 π / 2 1 − cos 2 ⁡ x...

myntfalskj4

myntfalskj4

Answered

2022-07-02

How does π / 3 π / 2 1 cos 2 x sin 2 ( x / 2 ) d x simplify to π / 3 π / 2 4 sin ( x / 2 ) cos 2 ( x / 2 ) d x?

Answer & Explanation

Kiley Hunter

Kiley Hunter

Expert

2022-07-03Added 7 answers

I = π 3 π 2 4 sin ( x / 2 ) cos 2 ( x / 2 ) d x = π 3 π 2 4 sin 2 ( x / 2 ) cos 2 ( x / 2 ) sin ( x / 2 ) d x
I = π 3 π 2 [ 2 sin ( x / 2 ) cos ( x / 2 ) ] 2 sin ( x / 2 ) d x
I = π 3 π 2 sin 2 ( x ) sin ( x / 2 ) d x
I = π 3 π 2 1 cos 2 ( x ) sin 2 ( x / 2 ) d x
I used 2 sin ( x / 2 ) cos ( x / 2 ) = sin ( x ) and 1 = sin 2 ( x ) + cos 2 ( x )
prirodnogbk

prirodnogbk

Expert

2022-07-04Added 6 answers

1 cos 2 x sin x 2 = sin 2 x sin x 2 = ( 2 sin x 2 cos x 2 ) 2 sin x 2 = 4 cos 2 x 2 sin x 2 .

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