9.3.3 More Integrating Tirgonometric Functions by Substitution Flashcards Preview

AP Calculus AB > 9.3.3 More Integrating Tirgonometric Functions by Substitution > Flashcards

Flashcards in 9.3.3 More Integrating Tirgonometric Functions by Substitution Deck (12):
1

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.

2

note

- 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.

3

Evaluate the integral.
∫secxtanx√1+secxdx

2/3(1+secx)^(3/2)+C

4

Integrate.∫cotxdx

ln | sin x | + C

5

Integrate.∫csc^2t / tan^2t dt

−cot^3t/3+C

6

Evaluate.∫8sin^33xcos3xdx

2/3sin^4 3x+C

7

Integrate.∫cos^4(x^2)sin(x^2)2xdx

−cos^5x^2/5+C

8

Integrate.∫tanxdx

ln | sec x | + C

9

Evaluate.∫tan^2θ/cos^2θdθ

tan^3θ/3+C

10

Integrate.∫sec(sinx)tan(sinx)cosxdx

sec (sin x) + C

11

Evaluate.∫sinxcosxdx

sin^2x/2+C

12

Evaluate the integral.∫cosxcos(sinx) dx

sin (sin x) + C

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