(a) = + 10. (b) = (c) = u x2 u x dx. u x2. 3. The best substitution for the integral is (a) = cos (b) = sin (c) = sin10 u x. u x. u x. If the substitution = tan is made then 4. u x (a) = sec (b) = sec2 (c) = sec2 du x dx. du x. du x dx. If the substitution = + + 1 is made then 5. u x8 x (a) = 8x (b) = (8x7 + 1)dx. (c) = du dx. du du x8 dx. 6. If the substitution u = x2 - 4 is used on the definite integral, then the new limits of integration are (a) = 0 and = -4. (b) = -4 and = 32. (c) = -4 and = 6. u u u u u u 7. If the substitution = 3x is used on the definite integral, the new limits of integration are u (a) = - and = (b) = - and = (c) = - and = . u u u u u u π π/2 π/2 π/2. π π 8. equals (f (a) ( + x))4 C. (f (f (b) ( + (c) '( + x))3 C. x))4 C. 9. To integrate, you should replace the integrand by (a) (1 + cos 5x)/2. (b) (1 - sin 5x)/2. (c) (1 + cos 10x)/2. 10. Evaluating the integral results in 4 (b) (c) Quick Quiz 5.5 Answers lc 2a 3b 4c 5b 6b 7a 8a 9e 10c
(a) u = x2 + 10. (b) u = x dx. (c) u = x2. 3. The best substitution for the integral is (a) u = cos x. (b) u = sin x. (c) u = sin10 x. 4. If the substitution u = tan x is made then (a) du = sec x dx. (b) du = sec2 x. (c) du = sec2 x dx. 5. If the substitution u = x8 + x + 1 is made then (a) du = 8x dx. (b) du = (8x7 + 1)dx. (c) du = x8 dx. 6. If the substitution u = x2 - 4 is used on the definite integral, then the new limits of integration are (a) u = 0 and u = -4. (b) u = -4 and u = 32. (c) u = -4 and u = 6. 7. If the substitution u = 3x is used on the definite integral, the new limits of integration are (a) u = - π and u = π/2 (b) u = - π/2 and u = π/2. (c) u = - π and u = π . 8. equals (a) (f ( x))4 + C. (b) (f ( x))3 + C. (c) (f '( x))4 + C. 9. To integrate, you should replace the integrand by (a) (1 + cos 5x)/2. (b) (1 - sin 5x)/2. (c) (1 + cos 10x)/2. 10. Evaluating the integral results in 4 (b) (c) Quick Quiz 5.5 Answers lc 2a 3b 4c 5b 6b 7a 8a 9e 10c
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