# a couple integrals

• Apr 17th 2008, 10:49 AM
rsanford
a couple integrals
1.
$
\int \frac{sinx}{cos^3x} dx
$

2. $\int x \sqrt {1-x} dx$

3. if F(x)= $\int_{0}^{\sqrt x} \sqrt {t^2+20} dx
$
find F'(16)

Hi, any help would be wonderful. I really need the explanation more than the answer, though.
• Apr 17th 2008, 10:57 AM
PaulRS
1. Subsitute $u=\tan(x)$ remember that $u'=\frac{1}{cos^2(x)}$

2. Subsitute $u=\sqrt[]{1-x}$

3. Define $G(x)=\int_0^{x}{t^2+20}dt$ so that $G(\sqrt[]{x})=F(x)$(1)
Now differentiate in (1) using the chain rule and remember that $G'(x)=x^2+20$
• Apr 17th 2008, 10:59 AM
TKHunny
What are your thoughts?

1. A substitution looks easy enough. u = ???

2. Begging for Integration by Parts if you want to learn something, but a simple substitution of everything under the radical might be a lot easier.

3. A derivative of an integral? Don't forget the Chain Rule. This one likely is ill-formed, Do you mean "dt"?

Let's see what you get.
• Apr 18th 2008, 12:21 PM
Moo
Hello,

For the first one, a substitution u=cos(x) is quite a valid way to solve it too ^^
• Apr 18th 2008, 01:20 PM
colby2152
Quote:

Originally Posted by Moo
Hello,

For the first one, a substitution u=cos(x) is quite a valid way to solve it too ^^

I would definitely follow this substitution. Follow PaulRS' advice on the 2nd integral.