Integral Problems NEWBIE

[karatekid_81]

I am new to integrals and I am sucking at them I dont know where to start. Can someone show me how to do this problem so that maybe I will see the example, thank you.

int of cos(x)^3 sin (x)^2 dx

 

[skeeter]

\(\displaystyle \L \cos^3{x} \cdot \sin^2{x} =\)

\(\displaystyle \L \cos{x} \cdot \cos^2{x}\cdot \sin^2{x} =\)

\(\displaystyle \L \cos{x} (1 - \sin^2{x}) \sin^2{x} =\)

\(\displaystyle \L \cos{x} (\sin^2{x} - \sin^4{x})\)

now let u = sinx ...

 

[stapel]

I am new to integrals and I am sucking at them I dont know where to start. Can someone show me how to do this problem so that maybe I will see the example, thank you.

There were plenty of examples in class and in your book, so I'm not sure why you think one more example will suddenly explain the entire topic to you...? :shock:

In case you were just exaggerating, here's a hint: Convert cos²(x) into 1 - sin²(x), multiply out, and integrate the two terms separately, using u = sin(x) so du = cos(x) dx. :idea:

Eliz.

 

[karatekid_81]

thanks for the help, i think i got it, is the answer -1/15sin(x^3) (3sinx^2-5) +c

 

[Deleted member 4993]

thanks for the help, i think i got it, is the answer -1/15sin(x^3) (3sinx^2-5) +c

No...

The correct answer should be:

\(\displaystyle \frac{1}{3}\ sin^3(x) - \frac{1}{5}\ sin^5(x) + C\)

 

[karatekid_81]

hmmm, O I Get what I did, thanks