College Calculus

What is the integral of cos^6x? I tried half angle identities but it didn't really help...

1. 👍 0
2. 👎 0
3. 👁 177
1. dx cos^n x = (1/n)cos^(n-1) sin x +[(n-1)/n] dx cos^(n-2) x
so
get cos^4 from cos ^6
then cos^2 from cos^4
then
dx cos^2 x = (x/2) + (1/4)sin 2x

1. 👍 0
2. 👎 0
posted by Damon

Similar Questions

1. Trig/Precalc

So I have two questions that have been puzzling me for quite some time and would really appreciate any help with either of them! (a) There are four positive intergers a, b, c, and d such that

asked by majorbill on January 4, 2015
2. Trig identies, Calculus

Use the identities cos^2 x + sin^2 x =1 and cos2x=cos^2 x -sin^2 x to show that cos^4 x -sin^4 x = cos2x Im not sure how, I can solve my problem with half angle identities but im not sure where to start with this.

asked by Anon on February 25, 2017
3. Trigonometry - Identities

If tan 2x = - 24/7, where 90 degrees < x < 180 degrees, then find the value of sin x+ cos x. I applied various identities and tried manipulating the problem to get sin x + cos x = sin(arctan(-24/7)/2) + cos(arctan(-24/7)/2) I also

asked by Sam on November 14, 2013
4. Trigonometry

Use the half-angle identities to find all solutions on the interval [0,2pi) for the equation cos^2(x) = sin^2(x/2)

asked by Nikki on July 15, 2012
5. Trigonometry

Use the half-angle identities to find all solutions on the interval [0,2pi) for the equation sin^2(x) = cos^2(x/2)

asked by Nikki on July 15, 2012
6. Precalculus

I've tried many times to get the equation to balance using trig identities like half-angle formulas, power-reducing formulas, and double angle formulas, but I couldn't get the equation to equal out. I only need to work one side to

asked by Christina on December 2, 2010
7. trig

1) Use double-angle identities to write the following expression, using trigonometric functions of x instead of 4x. cos 4x 2) Use half-angle identities to write the following expression, using trigonometric functions of x instead

asked by marie on May 28, 2012
8. tRiG/ AlGeBrA

1) Use double-angle identities to write the following expression, using trigonometric functions of x instead of 4x. cos 4x 2) Use half-angle identities to write the following expression, using trigonometric functions of x instead

asked by CHEYANNE on February 27, 2012
9. Integral

That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = -cos x du = cos x dx The integral is u v - integral of v du = -sinx cosx + integral of cos^2 dx which can be rewritten

asked by drwls on February 20, 2007
10. Integration by Parts

integral from 0 to 2pi of isin(t)e^(it)dt. I know my answer should be -pi. **I pull i out because it is a constant. My work: let u=e^(it) du=ie^(it)dt dv=sin(t) v=-cos(t) i integral sin(t)e^(it)dt= -e^(it)cos(t)+i*integral

asked by Ashley on April 16, 2015

More Similar Questions