(a) Explanation Given: I = ∫ − ∞ ∞ e − x 2 2 d x Calculation: First convert the integral into polar coordinates by substituting: x = r cos θ y = r sin θ d x d y = r d r d θ The corresponding limits in polar coordinates will be: 0 ≤ θ ≤ π 2 0 ≤ r ≤ ∞ Writing the double integral in polar coordinates: I = ∫ − ∞ ∞ e − x 2 2 d x ∫ − ∞ ∞ e − y 2 2 d y I 2 = ∫ − ∞ ∞ (b) To determine To Calculate: The value of the integral by using results in a).

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ISBN: 9781337275576

Author: Larson, Ron, Edwards, Bruce

Publisher: Cengage Learning,

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Chapter 14.3, Problem 63E

(a)

To determine

To calculate: The value of the integral I=∫−∞∞e−x22dx by converting to polar coordinates.

(b)

To determine

To Calculate: The value of the integral by using results in a).

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Chapter 14.3, Problem 62E

Chapter 14.3, Problem 64E

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The value of the integral I = ∫ − ∞ ∞ e − x 2 2 d x by converting to polar coordinates.