Ok, so you split up into two intervals I did from 2x to 0 and 0 to 4x.
Then you reverse the 2x to 0 and the integral becomes negative.
Then, replace 2x and 4x with u and chain rule
answer: (-2(x)^{2}-5/(2x)^{2}+5)*2 + (4(x)^{2}-5/(4x)^{2}+5)*4
Is my work correct? I was marked wrong and it said we didnt have to simplify.
Fundamental theorem, it says to find the derivative. So what I did was split up into two integrals because we have an x for both b and a of the integral. I split into intervals 2x to 0 and 0 to 4x. Since 2x is still on the bottom of integral, you move it by law of integrals to the top and it becomes a negative integral from 0 to 2x. Then I plugged in 2x and 4x in for each u value and did chain rule of 2x and 4x and got the answer from above. Sorry I don't know how to make integrals on the computer
My professor told us to split that's why I did it because he said when you have an x for both the top and bottom intervals you should split into two separate integrals. I guess you are saying some sort of rule that explains this without splitting it up?