Chapter 13: Q. 32 (page 1004)

Use definition to evaluate the double integral
$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$

Short Answer

Expert verified

The value of the integral is 126

Step by step solution

Given information

We are given a double integral

$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$

Use definition to find the value of double integral

We get,

$\sum_{i = 0}^{2} {\sum x^{2} y^{3}}_{j = 1}^{3} = \sum_{i = 0}^{2} (y^{3} + 4 y^{3} + 9 y^{3}) = \sum_{i = 0}^{2} (14 y^{3}) = 14 (1) + 14 (8) = 126$

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Use definition to evaluate the double integral
$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$

Short Answer

Step by step solution

Given information

Use definition to find the value of double integral

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Use definition to evaluate the double integral∫∫Rx2y3dAWhereR={(x,y)|1≤x≤3,0≤y≤2}

Short Answer

Step by step solution

Given information

Use definition to find the value of double integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Logic and Functions

Geometry

Statistics

Theoretical and Mathematical Physics

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Use definition to evaluate the double integral
$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$