Homework Statement
Evaluate the Improper integral [4,13] 1/(x-5)1/3
Homework Equations
N/A
The Attempt at a Solution
In step 1, I split the integral into two separate integrals because at x=5, it would be undefined. I made the first limit approach 5 from the left and the second limit...
Thank you so much! I should have noticed the reducing.
Finishing the problem:
sec-1(2) - sec-1(21/2)
sec-1(2) - sec-1(√(2))
This equals:
arccos(1/2) - arccos(1/√(2))
arccos(1/2) - arccos(√(2)/2)
pi/3 - pi/4 = pi/12
Homework Statement
[23/4, 2] 4/(x√(x4-4))
Homework Equations
∫ du/(u√(u2 - a2)) = 1/a(sec-1(u/a) + c
The Attempt at a Solution
I first multiplied the whole thing by x/x. This made the problem:
4x/(x2√(x4 - 4))
Then I did a u substitution making u = x2. Therefore, du = 2xdx. I multiplied by...