Homework Help: Integral invovling sec

1. Feb 24, 2008

kuahji

evaluate

$$\int2(sec x)^3$$ with the limits as -pi/3 to 0

I tried all sorts of things from breaking it apart to substitution, but known of what I tried work.

The book shows setting u=sec x & v=tan x

Then it shows the first step as 2 (sec x tan x) - 2 $$\int(sec x) * (tan x)^2 dx$$ then evaluate both parts to -pi/3 to 0.

Which is really what I'm not understanding. How did they integrate the first part & then still have the next part? I'm also not seeing how u & v come into play.

Guess I'm just plain lost on this one.

Last edited: Feb 24, 2008
2. Feb 24, 2008

alfredska

Substitution

As Griffith's puts it, paraphrased, you can move the derivative from one variable to the other under an integral, and you'll just pick up a minus sign and a boundary term.

Thus the equation:
$$\int_a^buv'dx=\left.uv\right|_a^b-\int_a^bu'vdx$$

3. Feb 24, 2008

rocomath

$$\int\sec x(\tan^{2}x+1)dx$$
$$\int\sec x\tan^{2}xdx+\int\sec xdx$$

$$u=\sec x$$
$$du=\sec x \tan x dx$$

$$dV=\tan^{2}xdx$$
$$V=\sec x$$

Last edited: Feb 24, 2008