Workshop #29 | Answer Key

University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

261

Pages:

2
Author:

Rose Newman

Workshop #29 d 3 x2 1. (a) Compute e . dx 2 (b) Which of the following integrals are you able to compute, just by having computed the above derivative? Z Z Z 3 x2 2 x2 e dx 3xe dx ex dx 2 Z 2. Consider the integral 3x2 sin(x3 ) dx. (a) If we let u = x3 , then what must go in the blank below? Z 3x2 sin(x3 ) dx = Z du (b) Do you think the new “du” integral will be easier, harder, or about the same difficulty to compute as the original “dx” integral? Z 3. Consider the integral 2 5xe4x dx. (a) If we let u = x2 , then what must go in the blank below? Z 5xe 4x2 Z dx = du (b) If we let u = 4x2 , then what must go in the blank below? Z 5xe 4x2 Z dx = du (c) If we let u = 2x, then what must go in the blank below? Z 5xe 4x2 Z dx = du (d) Do any of the new “du” integrals look like they will be easier to compute than the original “dx” integral? If so, which one(s)? 4. (a) If u = x2 , then what must go in the blank below? Z Z dx = sin u du u5 (b) If u = tan x, then what must go in the blank below? Z Z dx = u2 + 5u du 5. Compute the following integrals. Z p (a) x 5x2 + 2 dx Z √ (b) ex 2 + ex dx Z (ln x)5 (c) dx x Z ex (d) dx ex + 1