• # Revision:Further Integration

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Further Integration

## Hyperbolic Standard Integrals

### Inverse Trig and Hyperbolic Integrals

#### Reduction Formula

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 :

Find

take

The refers to the integral where there is a power of n involved.

Evaluating this by integration by parts:

So

Notice that

becomes

From this, we can find

by saying "let n = 3".

Therefore,

Therefore,

Therefore,

This can be used for and other trigonometric functions.

Arc Length AB =

Arc Length AB =

Arc Length AB =

### Area of Surface of Revolution

When rotated around the x axis:

Surface Area =

When using parametric coordinates (for rotation around the x axis):

Surface Area =

When rotated around the y axis:

Surface Area =