(c dx Since y=x?e-6x2 has a vertical asymptote at x=0, the integral is improper. Since y=x?e-6x2 has a vertical asymptote at x=e, the integral is improper. Since the integral has an infinite interval of integration, the integral is improper. O The integral is not improper. (d) 4cot(x) dx Since the integral has an infinite interval of integration, the integral is improper. Since y=4cot(x) has a vertical asymptote at x=", the integral is improper. O Since y=4cot(x) has a vertical asymptote at x=0, the integral is improper. The integral is not improper.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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Explain why each of the following integrals is improper.

(c)
-6x²
dx
Since y=x?e-6x² has a vertical asymptote at x=0, the integral is improper.
Since y=x?e-6x² has a vertical asymptote at
the integral is improper.
X=e,
Since the integral has an infinite interval of integration, the integral is improper.
The integral is not improper.
(d)
4cot(x) dx
Since the integral has an infinite interval of integration, the integral is improper.
Since y=4cot(x) has a vertical asymptote at x=,
the integral is improper.
6
Since y=4cot(x) has a vertical asymptote at x=0, the integral is improper.
The integral is not improper.
Transcribed Image Text:(c) -6x² dx Since y=x?e-6x² has a vertical asymptote at x=0, the integral is improper. Since y=x?e-6x² has a vertical asymptote at the integral is improper. X=e, Since the integral has an infinite interval of integration, the integral is improper. The integral is not improper. (d) 4cot(x) dx Since the integral has an infinite interval of integration, the integral is improper. Since y=4cot(x) has a vertical asymptote at x=, the integral is improper. 6 Since y=4cot(x) has a vertical asymptote at x=0, the integral is improper. The integral is not improper.
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