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Mathematical Expression Editor

Sample Tests for Chapter 1

Sample Test 1a

(problem 1) Compute

u-sub with

(problem 2) Compute

u-sub with

(problem 3) Compute

IBP

LIATE

Need IBP twice- try Tabular Integration

(problem 4) Compute

IBP

LIATE

(problem 5) Compute

Use the half angle formula twice

(problem 6) Compute

set aside to prepare for u-sub

convert remaining secants into tangents using

(problem 7) Compute

trig sub with

(problem 8) Compute

trig sub with

(problem 9) Compute

Partial Fraction (distinct linear factors)

(problem 10) Compute

Partial Fraction (repeated linear factor)

(problem 11) Compute

replace with and take the limit as approaches

to calculate the limit, remove the negative exponent

(problem 12) Compute

replace with and take the limit as approaches from the left

to calculate the limit, remove the negative exponent

Sample Test 1b

(problem 1) Compute

answer:

(problem 2) Compute

Write as and do u-sub with

answer:

(problem 3) Compute

answer:

(problem 4) Compute

use integration by parts twice to get back to the original integral ‘I’