University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

249

Pages:

1
Author:

Bidoggia5pt

Workshop #12 Z 1. Consider the integral x3 dx. 9 − 4x2 (a) Use regular substitution to compute this integral. (b) Use trig substitution to compute this integral. (c) In this case, which method do you think was easier? 2. (a) Find a pair of numbers to place in the numerators below so that the fractions are in simplest form and their sum is 11 12 . 11 + = 3 4 12 (b) Find a pair of numbers to place in the numerators below so that the fractions are in simplest form and their sum is 11 12 . 11 + = 6 4 12 (c) Find a pair of numbers to place in the numerators below so that their sum is x−1 + x+1 = x2 3 −1 Z (d) Use what you did in problem 2c to help you compute 3. Consider the rational expression 3 . x2 −1 x2 3 dx. −1 x3 − 6x2 + 2x + 30 . x2 − x − 6 (a) This rational expression is called improper because the degree on the bottom is not larger than the degree on the top. Perform long division so that we end up with a polynomial plus a rational expression that is proper. x3 − 6x2 + 2x + 30 =| x2 − x − 6 {z polynomial } + x2 − x − 6 (b) Find numbers to place in the numerators to make the equation below true. x−3 + x+2 = x2 3x −x−6 (c) Fill in the blanks below. x3 − 6x2 + 2x + 30 =| x2 − x − 6 Z (d) Compute Z 4. Compute x3 − 6x2 + 2x + 30 dx. x2 − x − 6 2x3 − x2 + 4 dx. x2 + 1 {z polynomial } + x−3 + x+2