A community for students.
Here's the question you clicked on:
 0 viewing
sha0403
 2 years ago
help me to integrate this.. integration of cos^3 x dx..
sha0403
 2 years ago
help me to integrate this.. integration of cos^3 x dx..

This Question is Closed

Asad0000
 2 years ago
Best ResponseYou've already chosen the best response.1split the cos^3x into cosx and cos^2x then use the trigonometric substitution. Replace cos^2x by (1  sin^2x). Now you can use some integrate it.

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0but i still did not get sin x  1/3 sin^3 (x)+c... bcoz the question ask to prove..

Asad0000
 2 years ago
Best ResponseYou've already chosen the best response.1Look. When you did the substitutions as I told you above, you should end up with the following integral:\[\int\limits_{}^{} [(1  \sin^{2}(x) )\cos(x) ]dx\]

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0int (1sin^2 x)cosx dx = int cosx dx  int sin^2 x cosx dx for int cosx dx = .... and to find int sin^2 x cosx dx, use int by sub, let u=sinx du = .... continue it

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0ok the i get integration of (cos x  u^2) du.. how to solve integration of cos x in term of u?

Asad0000
 2 years ago
Best ResponseYou've already chosen the best response.1if u = sin(x), then du = cos(x)dx. So replace the sin^2(x) in the original integral by u^2 and cos(x)dx by du. You will have a really trivial integral.

Eng.Mido
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits(\cos ^{3}{x})=\int\limits(cosx*\cos^{2}{x})=\int\limits(cosx(1\sin ^{2}{x})=\int\limits(cosx)(sinx)^2(cosx)=sinx1/3(\sin ^{3}{x})+\]

Eng.Mido
 2 years ago
Best ResponseYou've already chosen the best response.1a proof for my answer: cos^3x can be written as cos^2x*cosx. Then, we all know that cos^2x can be written as 1sin^2x. then we solve the bracket. then we'll find (sinx)^2*cosx , this remind us of the integration rule where [f(x)]^n*f'(x) = ([f(x)]^n+1/n+1)+c

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0but how to solve the integration of cos xu^2 du?

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0no.. like this integration of (cos x)(u^2) du

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.0@sha0403\[\Large \int\limits (1 \sin^2 x)(\cos x dx)\]let \(u=\sin x\), \(du = \cos x dx\)

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0yes but how ti integrate cos x in term of du?

Eng.Mido
 2 years ago
Best ResponseYou've already chosen the best response.1use the substitution method.

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0ok i get it now.. thank u..sorry i was too slow..

Eng.Mido
 2 years ago
Best ResponseYou've already chosen the best response.1\[\cos^2x*cosx dx=\cos^3x \]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.