Asked by alice
Evaluate the integral.
from 0 to π/2
sin^3(θ)cos^5(θ) dθ
from 0 to π/2
sin^3(θ)cos^5(θ) dθ
Answers
Answered by
Steve
The way this is done is to express everything in terms of sin or cos:
sin^3(θ)cos^5(θ) dθ
= sin^3θ cos^4θ cosθ dθ
= sin^3θ (1-sin^2θ)^2 cosθ dθ
Now let
u=sinθ
du = cosθ dθ
and you have
u^3 (1-u^2)^2 du
and it's a cinch...
sin^3(θ)cos^5(θ) dθ
= sin^3θ cos^4θ cosθ dθ
= sin^3θ (1-sin^2θ)^2 cosθ dθ
Now let
u=sinθ
du = cosθ dθ
and you have
u^3 (1-u^2)^2 du
and it's a cinch...
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.