Question

need help with integral problem

Answer 1

\[\int\limits_{0}^{\pi/4} 1+\cos^2 \theta/\cos^2 \theta\]

Answer 2

is the integrand (1+cos^2(theta))/cos^2(theta)?

Answer 3

im confused on how to do this one

Answer 4

yes

Answer 5

\[\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\]

Answer 6

\[\int\limits_{0}^{\frac{\pi}{4}}(\sec^2(\theta)+1)d \theta \]

Answer 7

so its 1/cos^2 theta + cos^2 theta/ cos^2 theta

Answer 8

yep

Answer 9

do you know how to integrate that expression?

Answer 10

no

Answer 11

what is the derivative of tan(x) (w.r.t x)?

Answer 12

sec^2?

Answer 13

\[\frac{d}{dx} \tan(x) =\sec^2(x) \\ \int\limits_{}^{}\sec^2(x) dx=\tan(x)+C\]

Answer 14

okay so its tan(x)+x

Answer 15

+C

Answer 16

and then yes