Hyperbolic Standard Integrals
Inverse Trig and Hyperbolic Integrals
The Reduction Formula is used when integrals can be reduced by generalising the integral for a function to the powers of n. From this you can substitute a value for n and evaluate a definite or indefinite integral relatively easy. They are especially useful when integrating large powers of trigonometric functions.
For example :
Evaluating this by integration by parts:
by saying "let n = 3".
Length of a Curve
Area of Surface of Revolution
When rotated around the x axis:
When using parametric coordinates (for rotation around the x axis):
When rotated around the y axis: