Trigonometric substitution  Integration Techniques
Trigonometric substitution
In this section, we will look at evaluating trigonometric functions with trigonometric substitution. A lot of people normally substitute using trig identities, which you will have to memorize. However, Dennis will use a different and easier approach. He will use the idea of Pythagoras Theorem and make a relation with sine and cosine in terms of x to substitute. In more advance questions, we will use Pythagoras Theorem to make a relation with tangent and secant to substitute. No matter what type of questions you do, you will only need to know Pythagoras Theorem and nothing else!
Lessons
Notes:
Prerequisite: Trigonometry Ratio: “SOHCAHTOA”

a)
$\int \sqrt{9x^2}xdx$

b)
$\int \sqrt{9x^2}dx$


2.
Evaluate the integral (Type A: $\sqrt{a^2x^2}$).

b)
$\int \frac{\sqrt{49x^2}}{x^2}dx$

3.
Evaluate the integral (Type B: $\sqrt{a^2+x^2}$).

b)
$\int \frac{x^3}{(16x^2+25)^{\frac{3}{2}}}dx$