Flashcards in 9.3.3 More Integrating Tirgonometric Functions by Substitution Deck (12):
More Integrating Trigonometric Functions by Substitution
• You can apply integration by substitution to integrands involving trigonometric functions that are not composite functions.
• When working with integrands that include trigonometric expressions, it is sometimes necessary to rewrite those expressions using trig identities.
- Instead of a composite function, this integral involves the product of two trigonometric functions.
- You could let u be sinx, in which case du would be cosx, or you could let u be cosx, making du be –sinx. You might want to choose u = sinx to avoid the negative sign.
- Once you have determined the expression for u, the integrand should be simple to evaluate. Remember to replace u with its expression in terms of x.
- You can check your work by integrating with the help of the chain rule.
- You may often find it useful to express trigonometric
integrands in terms of the sine and cosine functions.
- Notice that you must choose u = cosx, since it is in the denominator. That way the du-expression can replace the numerator and dx.
- Factor out the –1 from the integrand.
- The integral of du/u is ln|u| + C.
- Make sure to express your result in terms of x.
- Check that your answer is correct by integrating.
Evaluate the integral.
ln | sin x | + C
Integrate.∫csc^2t / tan^2t dt
ln | sec x | + C
sec (sin x) + C