Question

integral from 0 to 2 of (5-((4-x^2)^(1/2))

Answer 1

did you try to substitute
\(x=2\sin u\)
?

Answer 2

dx= ... ?
4-x^2 =... ?

Answer 3

Yup. I got to the integral of 4cos^2x, but am a little stuck on this part...

Answer 4

(5-2cos u)(2 cos u) du

how did u just get 4 cos^2 u ?

Answer 5

i get 10 cos u -4cos^2 u du

Answer 6

hah, my bad, I pulled out the 5 as a separate integral

Answer 7

but where you are is where I'm stuck

Answer 8

cool
so,
cos^2 u
write that in terms of cos2u, can u ?

Answer 9

know the formulas for cos 2x ?

Answer 10

I don't...there's a formula?

Answer 11

I don't understand how I can write cos^2u in terms of cos(2u)

Answer 12

yup

\(\large \cos2x=\cos^2x-\sin^2x=2\cos^2x-1=1-2\sin^2x\)

heard of them ?

Answer 13

so, from cos2x = 2 cos^2x-1
could you isolate cos^2 x???

Answer 14

You mean from the 4?

Answer 15

i just mean, whether you can isolate cos^2x from
cos2x = 2 cos^2x-1
?

Answer 16

I don't know, the concept is foreign to me,

Answer 17

cos2x = 2 cos^2x-1
so,
cos^2 x = (cos 2x+1)/2

just simple algebra

Answer 18

\(\int 4\cos^2x dx = 4\int\dfrac{\cos2x+1}{2}dx \)
and can you integrate cos 2x and 1 ?

Answer 19

ahh okay I got it!

Answer 20

I'm good from here, was just confused on that step!

Answer 21

thanks !

Answer 22

welcome ^_^
and
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