   Chapter 15.1, Problem 49E

Chapter
Section
Textbook Problem

Use symmetry to evaluate the double integral.49. ∬ R x y 1 + x 4 d A ,   R = { ( x , y ) | − 1 ≤ x ≤ 1 , 0 ≤ y ≤ 1 }

To determine

To find: The value of given double integral over R .

Explanation

Given:

The function is f(x,y)=xy1+x4 .

The rectangle, R=[1,1]×[0,1] .

Definition used:

Odd function: If f is a function and f(x)=f(x) , then f is said to be an odd function.

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

If f is an odd function, then aaf(x)dx=0 (2)

Calculation:

Compute the value of the given double integral by using equation (1)

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