How to Do an Area Approximation Using Sigma Notation
The Sum Rule, the Constant Multiple Rule, and the Power Rule for Integration
How to Find the Volume and Surface Area of Gabriel's Horn

Integration by Parts Problems where You Go around in Circles

Sometimes if you use integration by parts twice, you get back to where you started from — which, unlike getting lost, is not a waste of time.

image0.png

First, use the LIATE mnemonic device to pick your u:

image1.png

To pick your u, go down this list in order; the first type of function on this list that appears in the integrand is the u.

image2.png

Now fast forward to the formula step:

image3.png

Now, substitute the right side of the above equation for the

image4.png

from the original solution:

image5.png

You can now solve this equation for the integral

image6.png

Use I in place of that integral to make this messy equation easier on the eyes:

image7.png

Add I to both sides:

image8.png

Multiply both sides by 1/2:

image9.png
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Integrate When the Powers of Sine, Cosine Are Even, Nonnegative
How to Solve Improper Integrals for Functions that Have Vertical Asymptotes
The Riemann Sum Formula For the Definite Integral
Solve Improper Integrals with One or Two Infinite Limits of Integration
Solving Integration Problems in Calculus
Advertisement

Inside Dummies.com