Thread: 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.

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.

$\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?

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.

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

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.