Chapter Contents

Comments, Questions?

Follow IntMath on Twitter

Get the Daily Math Tweet!
IntMath on Twitter

Recommendation

Easy to understand calculus lessons on DVD. Try before you commit. More info:
MathTutorDVD.com

From the math blog...

What did Newton originally say about Integration? (19)

What did Isaac Newton's original manuscript look like? What did it say?...

Friday math movie - Trigonometric Graphs (16)

Here's a light-hearted introduction to the concepts of trigonometric graphs....

Tanzalin Method for easier Integration by Parts (16)

Getting lost doing Integration by parts? Tanzalin Method is easier to follow, but doesn't work for all functions....

Friday math movie - Trigonometric Strange Attractor Evolution (15)

5D forces
This week's movie is a representation of a 5-dimensional space acted on by 5-D forces.
...

The locus and the ellipse (7)

ellipse0
A reader from Chile provides an explanation of the locus of the center of an ellipse which moves such that it is tangent to the positive x- and y-axes....

6. Integration: Inverse Trigonometric Forms

by M. Bourne

Using our knowledge of the derivatives of inverse trigonometric identities that we learned earlier and by reversing those differentiation processes, we can obtain the following integrals:

Example 1: Integrate: .

Answer

Example 2: Integrate:

Answer

Example 3: Find the area bounded by the curve and the lines x = 0, y = 0 and x = 2.

Here is the LiveMath solution to this problem:

LIVEMath

Answer

Caution:

There are a number of integrals of forms which look very similar to the above but are actually different, e.g.

We will develop methods to solve these in a later section. (See Integration by Trigonometric Substitution.)

Exercises

Integrate each of the given functions:

1. math expression

Answer

2. math expression

Answer

3. math expression

Answer

4. Find the area bounded by the curve and the lines x = 0, y = 0 and x = 1.

First, the LiveMath solution to this problem:

LIVEMath

Answer

This is not the answer ... it is a corruption of a .gif file containing the answer!!:

math expression

[This happened in MS Word during a period of great instability - the computer's and mine...]

5. Integration: Other Trigonometric Forms

7. Integration by Parts

Didn't find what you are looking for on this page? Try search:

Find your integral using Wolfram|Alpha!

This next search box allows you to enter your math problem and Mathematica solves it for you. (It's free!)

See how to enter math.

Calculus Lessons on DVD

Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

Bookmark this page

Add this page to diigo, Redditt, etc.

Like Us on Facebook!

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Need a break? Play a math game. Well, they all involve math... No, really!