Example 2: Trigonometric Substitution

Find ∫√(x² - a²) dx.

Figure 7.6.3

Let θ = arcsec (x/a) (Figure 7.6.3), so

x = asec θ, dx = a tan θ sec θ dθ, = a tanθ.

So

This is as far as we can go on this problem until we find out how to integrate ∫ sec θ dθ in the next chapter.