Integrating Trig Functions
How do I integrate sin, cos and sec^2?
- The integrals for sine and cosine are
where is the constant of integration
- Also, from the derivative of
- For the linear function, where and are constants,
- For calculus with trigonometric functions angles must be measured in radians
Examiner Tip
- Remember to add 'c', the constant of integration, for any indefinite integrals
Worked example
a)
Find, in the form, an expression for each integral
i.
ii.
i. This is a result you should be able to recall from memory.
ii. Use the standard result:
b)
A curve has the following equation:
The curve passes through the point with coordinates
Find an expression for
Factor out the 2 in front of the sin first, and then use the standard result:
When multiplying the arbitrary constant , by 2, it is still just an arbitrary constant and so it is still just written as
Substitute in the given coordinate, and evaluate, to find
At
Rewrite the full expression for