Section 7.3

7.3 Trigonometric Substitution

Key Concepts

When expression of the form:

(a²-x²)^1/2
(x²-a²)^1/2
(a²+x²)^1/2
(a²+x²)

occur, it is often useful to make a change of variable,

x = a sin(t)
x = a sec(t)
x = a tan(t)
x = a tan(t)

respectively. Substitution for x, and computing dx, yields a trigonometric integral which can be handled by the methods of the previous section, section 7.2 .

Note: This method of integration is best learned by practice. Solve as many of the problems on pages 22 and 23 as possible!

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