Integration of Trigonometric functions

Level 1

Integrate the following functions with respect to x.

a) cos(x)

b) sin(x)

l1q

 

Solution

a) Recall that, the function that was differentiated to get cos(x) was sin(x).

le1

b) This is a bit tricky.  cos(x) was differentiated to getsin(x), not sin(x).

 

l1b

 

c) This is straightforward as in (a) above.

l1c

 

Integration Techniques.

A) Simplification : Some trigonometric functions may seem difficult to integrate if they are not in their simplest form. Hence, a wise thing to do is to simplify before integrating. Your knowledge of double angles, compound angles and trigonometric identities is an advantage to you.

Example

Calculate:

12al2b

Solution

l2asl2bs

Now try this one.

Calculate:

l2c

If you need help, then view or download the solution.