Compute <msubsup> &#x222B;<!-- ∫ --> 0 <mrow class="MJX-TeXAtom-ORD"> &#x0

Gauge Terrell 2022-07-10 Answered
Compute 0 π / 2 cos x 2 sin 2 x d x
You can still ask an expert for help

Want to know more about Trigonometry?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Kathryn Moody
Answered 2022-07-11 Author has 10 answers
Hint:
Knowing that sin 2 x = 2 sin x cos x and sin 2 x + cos 2 x = 1. The integral can be expressed as
I = 0 π / 2 cos x 1 + ( sin x cos x ) 2   d x
then use substitution x π 2 x, we have
I = 0 π / 2 sin x 1 + ( sin x cos x ) 2   d x
Add the two I's and let u = sin x cos x

We have step-by-step solutions for your answer!

Cierra Castillo
Answered 2022-07-12 Author has 6 answers
I = 0 π / 2 cos x 2 sin 2 x d x = 0 π / 2 cos x 2 2 sin x cos x d x = 0 π / 2 cos x 1 + cos 2 x 2 sin x cos x + sin 2 x d x = 0 π / 2 cos x 1 + ( cos x sin x ) 2 d x = 1 2 ( 0 π / 2 cos x 1 + ( cos x sin x ) 2 d x + 0 π / 2 sin x 1 + ( cos x sin x ) 2 d x ) = 1 2 0 π / 2 cos x + sin x 1 + ( cos x sin x ) 2 d x = 1 2 0 π / 2 d ( cos x sin x ) 1 + ( cos x sin x ) 2 = 1 2 arctan ( cos x sin x ) | 0 π 2 = π 4

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions