   Chapter 8.8, Problem 35E

Chapter
Section
Textbook Problem

Evaluating an Improper Integral In Exercises 33–48, determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. ∫ 0 2 1 x − 1 3   d x

To determine
Whether the improper integral 021x13dx converges or diverges.

Explanation

Consider the provided integral,

021x13dx=011x13dx+121x13dx=limb10b1x13dx+lima1+a21x13dx

Now, use the formula:

abf(x)dx=limca+cbf(x)dxabf(x)dx=limcbacf(x)dx

Then,

021x13dx=limb10b1x13dx+lima1+a21x13dx=limb10b(x1)1/3dx+lima1+a2(x1)1/3dx

Let x1=u. Then, dx=du

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