Question

please help!! Integral using inverses

Answer 1

\[\int\limits_{0}^{\sqrt{3}} \frac{ dx }{ \sqrt{4-x^2} }\]

Answer 2

HI!!

Answer 3

Hello :D

Answer 4

looks pretty much like an arcsine right?

Answer 5

yup!

Answer 6

in fact, if it was \[\int \frac{dx}{\sqrt{1-x^2}}\] it would be arcsine

Answer 7

mhm i'm having trouble trying to factor out the 4 :S

Answer 8

\[4-x^2=4(1-\frac{1}{4}x^2)=4(1-(\frac{x}{2})^2\]

Answer 9

so would there be a sqrt over the 4?

Answer 10

yeah, that was just the algebra under the radical

Answer 11

Misty's presentation needs one more right parenthesis:

\[4-x^2=4(1-\frac{1}{4}x^2)=4(1-(\frac{x}{2})^2)\]

Answer 12

ah okay

Answer 13

so then u would just be x/2 ?

Answer 14

the four will come out of the radical as a two

Answer 15

yup, you can do a u - sub and change the limits of integration while you are at it

Answer 16

ah okay i got it! That's mainly what was confusing me xD Thank you!!

Answer 17

I got pi/3 btw which i just put in and was right :)

Answer 18

\[\color\magenta\heartsuit\]

Answer 19

yay

Answer 20

Thank you!