Answers for Math 166T Practice for Midterm

Part I - No calculators

1. (Evaluate integrals of trigonometric functions .)

Type 1 and Type (a) If some function have odd degrees, then Step 1. Factor out sin x or cos x from the function with odd degree Step 2. Apply sin2 x + cos2 x = 1 to the function where the factor came from Step 3. Use a substitution , u = cos x or sin x which is not the factor (b) If all functions have even degrees, then use Half-angle Identity

2. (Use trigonometric and rationalizing substitutions to evaluate integrals.)

1) Integral involving 2) Integral involving 3) Integral involving 4) Integral involving

3. (Carry out integration by parts and apply it to evaluate integrals.)

Remember the LIATE rule .

4. (Use partial fractions to evaluate integrals of rational functions.)

Step 1. If the degree of numerator is at least that of denominator , then get a proper rational function by long division . Step 2. Factor D(x). Step 3. Do the partial fraction decomposition. Step 4. Integrate term by term .