1. ## Integration

If F(x) = $\displaystyle integral((-12sin(x))/ (cos^2(x))dx) + C$ F(0)= -4 Find C

Im sorry I dont know how to type for the integral symbol.

I would like to know how to start this problem. An explanation would be great.

2. Originally Posted by CalcGeek31
If F(x) = $\displaystyle integral((-12sin(x))/ (cos^2(x))dx) + C$ F(0)= -4 Find C

Im sorry I dont know how to type for the integral symbol.

I would like to know how to start this problem. An explanation would be great.
Let $\displaystyle u = \cos x$ and transform the integral to one that is solvable.

3. $\displaystyle F(x) = \int \frac{-12\sin{x}}{\cos^2{x}} dx + C$

$\displaystyle F(x) = -12\int \sec{x} \tan{x} \, dx + C$

can you finish?

4. Originally Posted by skeeter
$\displaystyle F(x) = \int \frac{-12\sin{x}}{\cos^2{x}} dx + C$

$\displaystyle F(x) = -12\int \sec{x} \tan{x} \, dx + C$

can you finish?
Definitely easier than mine.

5. but when you take that integral wouldnt it get -12(answer to integral) + C+ C or can you combine the C's

6. Originally Posted by CalcGeek31
but when you take that integral wouldnt it get -12(answer to integral) + C+ C or can you combine the C's
C is arbitrary (at first) so they can be combined.