Tuesday

September 23, 2014

September 23, 2014

Posted by **Michael** on Monday, December 1, 2008 at 3:54pm.

- calc -
**Reiny**, Monday, December 1, 2008 at 4:16pmy' = 20 * (sinx)^3 * (cosx)^2

= 20 sinx(sinx)^2(cosx)^2

= 20sinx(1 - cos^2 x)cos^2 x

= 20sinx cos^2 x - 20sinx cos^4 x

y = -20/3(cos^3 x) + 20/3(cos^5 x) + C, where C is a constant

- calc -
**Damon**, Monday, December 1, 2008 at 4:21pmlet u = sin^2 x

then du = 2 sin x cos x dx

let dv = -3 sin x cos^2 x dx

then v = cos^3 x

u dv = -3 sin^3 x cos^2 x dx

so

let u = -20/3 sin^2 x

then du = -40/3 sin x cos x dx

let dv = -(1/3)sin x cos^2 x dx

then v = cos^3 x

now by parts

int u dv = u v - int v du

int (20 sin^3 x cos^2 x dx) =

-(20/3)sin^2 x cos^3 x +(40/3)int(cos^4 x sin x dx)

well remember the first term at the end and the (40/3) and work on the integral

int cos^4 x sin x dx = -(1/5)cos^5 x

I think you can get it from there

**Answer this Question**

**Related Questions**

Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...

Calculus - Use the symmetry of the graphs of the sine and cosine functions as an...

Trig........ - I need to prove that the following is true. Thanks (cosx / 1-sinx...

Calculus - I don't know if I did these problems correctly. Can you check them? ...

Trigonometry Check - Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [...

Pre-calc - prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i ...

Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...

Math - Verify the identity . (cscX-cotX)^2=1-cosX/1+cosX _______ sorry i cant ...

Math - Pre- Clac - Prove that each of these equations is an identity. A) (1 + ...

trigonometry - can i use factoring to simplify this trig identity? the problem ...