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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Determining Whether an Integral Is Improper In Exercises 1-6, decide whether the integral is improper. Explain your reasoning.

0 1 2 x 5 x 2 5 x + 6 d x

To determine

Whether the integral 012x5x25x+6dx is improper.

Explanation

Given Information:

The limit is provided as:

012x5x25x+6dx.

Consider provided integral;

The Conditions for improper integral abf(x)dx. are;

1. Any of the limits of integral is infinity.

2. It consist of an infinite discontinuity in the integral [a,b]

If the integral satisfied any of the above condition, it is an improper integral.

As None of the limit of the integral is infinity. So, it doesn’t satisfy first condition.

The integrand is ratio form, so the value will have an infinite discontinuity if the denominator of the function will be zero.

So, Equate denominator of integral to zero as;

x25x+6=0x23x2x+

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