   Chapter 15.2, Problem 60E

Chapter
Section
Textbook Problem

Use Property 11 to estimate the value of the integral.60. ∬ T sin 4 ( x + y )   d A , T is the triangle enclosed by the lines y = 0, y = 2x, and x = 1

To determine

To estimate: The value of given double integral by property 11.

Explanation

Property used:

If mf(x,y)M for all (x,y) in D then, mA(D)Df(x,y)dAMA(D) .

Here, the constants are denoted by m, and M.

The area of the given region D is denoted by A(D) .

Given:

The function, f(x,y)=sin4(x+y) .

The region T is the triangle enclosed by the lines y=0,y=2x,x=1 .

Calculation:

From the given condition, it is observed that 0sin4(x+y)1 .

The region T is a triangle with vertices (0,0),(1,0),(1,2)

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