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: 
.
Example 2: Integrate: 
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:
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. 
2. 
3. 
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:
This is not the answer ... it is a corruption of a .gif file containing the answer!!:
[This happened in MS Word during a period of great instability - the computer's and mine...]
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