(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.

(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.

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Conic Sections

Section8.2: More Parabolas And Some Circles

Problem 63.1PS

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Question

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.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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