Integrals involving trig functions?

Question

please evaluate the following

integral (-pi/4 to pi/4, [(x-1) / (cos^2 x)]dx)

This is for exam prep .. it is not an assignment.

Answer 1

Ah Come on, nckobra40. He has not cheated until he gets an actual answer and uses it on his assignment.

For now, he can only be charged with:
attempted cheating,
conspiracy to cheat,
integrating without a licence, and
(this is ugly, better shield your eyes)

squaring a cosine in the denominator.

He could avoid hasher punishment by splitting the integral in two:

x/cos^2 and -1/cos^2

the second one would give -(tan x) to be evaluated from -pi/4 to +pi/4

Or, he could be convinced to give up on his accomplice cos^2 and turn him in (to something else, using trig identities).

I wonder if he'll do it.

Answer 2

start up with writing the imperative, that's x/sqrt(a million-16x^4) dx. you realize u=4x^2, so locate du in terms of dx. du/dx=8x, so dx=du/8. substitute du/8 in on your dx in the imperative. you will see it simplifies to a million/8 circumstances the imperative of a million/sqrt(a million-16x^4) du. substitute u into the imperative now, the place u^2 = 16x^4. The imperative now will become a million/sqrt(a million-u^2) du, that's arcsin(u/a million). So your answer will grow to be a million/8 * arcsin(u/a million), and substituting in x^4 for u, you will acquire a million/8arcsin(4x^2)

Answer 3

Dum dum. do your own homework. I'm forwarding this to your teacher and having you expelled for cheating