Question

integral sec^4 (x/2) dx from 0 to pi/2

Answer 1

you deleted the older post..

Answer 2

\[\int\limits_{?}^{?}\sec^4(\frac{x}{2})dx\]

Answer 3

sec^2 * sec^2(x) and change one into tangent

Answer 4

or tan i mean

Answer 5

then you will have a derivative and it's function

Answer 6

anyway apply integration by parts and simplify\[I = 2\sec^2(x/2) \tan(x/2) - 4I + 4\int\limits\limits_{}^{} \tan(x/2) \sec^2(2x/2)dx\] to get

Answer 7

\[\cos^2+\sin^2=1\]
\[1+\tan^2=\sec^2\]

Answer 8

eww that is ugly...

Answer 9

\[5I = 2\sec^2(x/2) \tan(x/2)+ 8\sec^2(x/2)\]
on applying limits we get
-3/5

Answer 10

sec^4(x/2) dx
u=x/2
du=1/2 dx
2du=dx
2/cos^4 (u) du

Answer 11

double susdtitution

Answer 12

you could do double substitution but i still believe splitting the sec up and then creating two integrals from that

Answer 13

ok

Answer 14

like this\[\int\limits_{?}^{?}\tan^2(x/2)\sec^2(x)dx +\int\limits_{?}^{?}\sec^2(x)dx\]

Answer 15

i mean x/2 for the other one

Answer 16

u = tan(x/2)
du = 1/2(sec^2(x/2)dx

Answer 17

2du=sec^2(x/2)dx and then you have just integral of u^2

Answer 18

the second one you can just take the integral it will just be tan(x/2)

Answer 19

or double substitution.,..... but parts seems a little insane. it'd work but that would be a lot of evaluating