Question

need help on the attachment @MIT 18.01 Single …

Answer 1

If I told you 1/cos^2(x) is equal to sec^2(x) making that term 3sec^2(x). Would that help you?

Answer 2

is that trig identity

Answer 3

yes

Answer 4

how is 1/cos^2 s equal to sec^2(x) through trig identity

Answer 5

\[\int \frac{3}{\cos^2 \theta}-2\sin\theta d \theta=\int 3\sec^2\theta-2\sin\theta d\theta\]
\[=3\int\sec^2\theta d\theta-2\int\sin\theta d\theta\]
I assume you can take it from there... I left off the limits, but they are the same the whole time.

Answer 6

what happen to the sin too?

Answer 7

\[\sec \theta=\frac{1}{\cos \theta}\]

That's the definition of secant.

Answer 8

agreene made the integral two separate integrals to make it easier to calculate. The sine is still there.

Answer 9

do I take the anti-derivative of sec^2(x) which is tan x and sin x which -cos x

Answer 10

yep and don't forget your coefficients.

Answer 11

ok

Answer 12

Did you find the answer?

Answer 13

yes it 2squrt(3)-2

Answer 14

how bout this new attachment