Trigonometric Substitution for Integrals: Example 1

in mathematics •  2 months ago  (edited)

In this video I go over an example on trig substitution for integrals and solve for the integral of the function sqrt(9-x2)/x2. In this example I write the variable x in terms of a sine function to simplify the integral by removing the square root.

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Trigonometric Substitution for Integrals: Example 1

Trigonometric Substitution Example 1.jpeg



Since this is an indefinite integral, we must return to the original variable x. This can be done by using trigonometric identities to express cotѲ in terms of sinѲ = x/3 or by drawing a diagram where Ѳ is considered as the angle of a right triangle. The latter is usually easier and we will try that:

Note: Although Ѳ > 0 in the diagram, this expression for cotѲ is valid even when Ѳ < 0.

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