The integral S dx √x(1+x) is improper for two reasons: The interval [0, ∞) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows. · So √x (1 + x) ' - √x (² + x)" dx = dx √x(1+x) X Need Help? Read It Watch It dx +

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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The integral
So® √X(₁²
dx
√x(1 + x)
is improper for two reasons: The interval [0, ∞) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as
follows.
So ² √x (1² + x)²
-6²
dx +
1/²
dx
√x(1 + x)
√x(1 + x)
Read It
Need Help?
dx =
Watch It
Transcribed Image Text:The integral So® √X(₁² dx √x(1 + x) is improper for two reasons: The interval [0, ∞) is infinite and the integrand has an infinite discontinuity at 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows. So ² √x (1² + x)² -6² dx + 1/² dx √x(1 + x) √x(1 + x) Read It Need Help? dx = Watch It
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