   Chapter 6, Problem 53RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating an Improper Integral In Exercises 51–56, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ∫ − ∞ 0 1 8 − x 3   d x

To determine

To calculate: The value of integral 018x3dx if it converges.

Explanation

Given Information:

The provided expression is,

018x3dx

Formula used:

From definition of improper integral.

If on the interval (,b], the function is continuous, then

bf(x)dx=limaabf(x)dx

Here, the improper integral converges if the limit exists and otherwise it diverges.

The integral formula

xndx=xn+1n+1+C

Calculation:

Consider the provided expression,

018x3dx

Use the definition of improper integral bf(x)dx=limaabf(x)dx

And simplify as:

018x3dx=limaa018x3dx

In the integral,

Assume 8x=u

Differentiate both the sides

dx=du

Now, substitute the values and integrate as:

18xdx=1u3du=32u23+C

Again, substitute the value of u

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