How do you integrate #int (3x)/sqrt((1-x^2))dx# using trigonometric substitution?

↳Redirected from "Which following pairs of atoms, have a lower electron affinity? a) Ca,K b) I,F c) Li, Ra. I seriously don't know anything about electron affinity all ik that it can buy another element"
1 Answer
Ken Rubenstein
Jan 24, 2016

You need to use the beautiful Pythagorean right triangle.

Here is the general antiderivative :
#-3*sqrt(1- x^2)#

Explanation:

Here's a quick paint job to show you the lovely right triangle:

enter image source here

You now need to find the following:

#1)x#

#2)dx/(d theta)#

#3)sqrt(1-x^2)#

I'll give you a gentle and loving push in the right direction:

What is x?

Well, it sure looks to be :

#x = sin (theta)#

Your turn!

Related questions
See all questions in Integration by Trigonometric Substitution
Impact of this question
6827 views around the world
You can reuse this answer
Creative Commons License