Question

calc help!

Answer 1

\[\int \sec(x)\tan(x)dx\]This is an identity. \[\frac{d}{dx} (\sec(x)) = \sec(x)\tan(x) \implies \ \int \sec(x)\tan(x) = ~?\]

Answer 2

Example:\[\frac{d}{dx} (\cos(x)) = -\sin(x) \implies \int \sin(x)dx = -\cos(x) +C\]

Answer 3

1/cos(x)+C

Answer 4

....no.

Answer 5

Carefully look at the example I provided you with.

Answer 6

You will see that if you integrate the derivative of a function, you will end up with the function you were taking the derivative of.

Answer 7

Example 2: \[\frac{d}{dx}(\cot(x)) = -\csc^2(x) \implies \int csc^2(x)dx = -\cot(x)+C\]

Answer 8

-sec(x)+C

Answer 9

The only ones that are negative are all the "C" functions you take the derivative of: i.e. \[\cos(x)\]\[\cot(x)\]\[\csc(x)\]

Answer 10

so my final answer should be tan(x)+C

Answer 11

What is the derivative of \(\sec(x)\)?

Answer 12

Let's start here.

Answer 13

Once you know the derivative, you will know what the integral will yield.

Answer 14

sec(x)tan(x)

Answer 15

oh so it would be sec(x)+C

Answer 16

Therefore, the integral of \(\sec(x)\tan(x) = \sec(x)~ \checkmark\)

Answer 17

Goodjob.

Answer 18

thank you (: