Chapter 13: Q. 64 (page 1005)

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
$f (x, y) = x^{2} y e^{x y} W h e r e R = {(x, y) | 0 \leq x \leq 1, 0 \leq y \leq 2}$

Short Answer

Expert verified

The integral does not converge

Step by step solution

Given information

We are given a rectangular region

$f (x, y) = x^{2} y e^{x y} W h e r e R = {(x, y) | 0 \leq x \leq 1, 0 \leq y \leq 2}$

Evaluate the integral

We get,

$\int_{R} x^{2} y e^{x y} d A = \int_{0}^{2} \int_{0}^{1} x^{2} y e^{x y} d x d y = \int_{0}^{2} {[x^{2} - \frac{2 x}{y} e^{x y}]}^{1}_{0} d y = \int_{0}^{2} [1 - \frac{2}{y} e^{y}] d y = \infty$

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Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
$f (x, y) = x^{2} y e^{x y} W h e r e R = {(x, y) | 0 \leq x \leq 1, 0 \leq y \leq 2}$

Short Answer

Step by step solution

Given information

Evaluate the integral

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Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane f(x,y)=x2yexyWhereR={(x,y)|0≤x≤1,0≤y≤2}

Short Answer

Step by step solution

Given information

Evaluate the integral

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Most popular questions from this chapter

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Logic and Functions

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Study anywhere. Anytime. Across all devices.

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane
$f (x, y) = x^{2} y e^{x y} W h e r e R = {(x, y) | 0 \leq x \leq 1, 0 \leq y \leq 2}$