# college

posted by .

from 0 to (π/2) ∫(sin^3⁡θ cos^3⁡θ dθ)

• Math, not "college" -

Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.

• Integral calculus -

When the sin/cos are in odd powers, use the substitution
cosθdθ=d(sinθ), or
sinθdθ=-d(cosθ)

∫sin³θcos³θd&theta (from 0 to π/2)
=∫sin³θ(1-sin²θ) (cosθdθ)
=∫(sin³θ-sin5θ)(d(sinθ)) (from 0 to sin(π/2))
=[sin4θ/4-sin6θ/6](from 0 to 1)
=1/12

## Similar Questions

1. ### Math - Calculus

The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a …
2. ### trig

cosθ =5/13 with -π/2 < θ <0 find each of the following sin( θ - 5π/4) cos( θ - 11π/6) tan( θ + 5π/4) can some1 explain to me how to do these?
3. ### math

if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?
4. ### trigonometry

if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?

6. ### Calculus AP

hi again im really need help TextBook: James Stewart:Essential Calculus, page 311. Here the problem #27: First make a substitution and then use integration by parts to evaluate the integral. Integral from sqrt(pi/2) TO sqrt(pi)of θ^3 …
7. ### Precalc/Trig

Sorry there are quite a few problems, but I just need to know if these are correct (and if they aren't, where I went wrong): 1. Solve these equations. tanθ = -√3 θ = 2π/3 + kπ θ = 5π/3 + kπ …
8. ### math

Given that sinθ = 2/3 and is an acute angle. Find: Tanθ giving your answer in surd form θ = tan^(-1)⁡〖(2/√5)= 41.81°〗 Sec^22 θ θ= cos^(-1)⁡〖(3/√5〗)=
9. ### math

Simplify the trigonometric function sin^4⁡x-cos^4⁡x cos^2⁡â-sin^2⁡â=1+2cos⁡â (1+cot^2⁡x )(cos^2⁡x )=cot^2⁡x cot^2⁡t/csc⁡t =(1-sin^2⁡t)/sin⁡t (Work on both sides!) …
10. ### Math

What is the value of sin⁡2x given that sin⁡x+cos⁡x+tan⁡x+cot⁡x+sec⁡x+csc⁡x=7?

More Similar Questions