Lecture #9

Today, we completed the discussion of trigonometric integrals, which are integrals with integrands being

  • powers of cosine times powers of sine; or
  • powers of tangent times powers of secant.

Other type of trigonometric integral may be converted to the above types, and cotangent / cosecant pairs follow similar rules. The scan is here: wk4day9.

The above are especially important because they come up in important integrals in applications involving

  • \(\sqrt{a^2-x^2}\)
  • \(\sqrt{a^2+x^2}\)
  • \(\sqrt{x^2-a^2}\)

which arises when dealing with circles, ellipses and right-angled triangles, for instance.

The integration of function with the above terms will require a new type of substitution, which is an inverse substitution using trigonometric functions. This topic is called integration by trigonometric substitution and will not be tested in midterm 1.

Posted in Lecture

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