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Chapter 13: Q. 61 (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)=sinxcosyWhereR={(x,y)|0鈮�x鈮�蟺,0鈮�y鈮�蟺}

Short Answer

Expert verified

The value of the integral is 0

Step by step solution

01

Given information

We are given a region

f(x,y)=sinxcosyWhereR={(x,y)|0鈮�x鈮�蟺,0鈮�y鈮�蟺}

02

Find the volume

We are given

鈭�Rsinxcosy=鈭�0蟺鈭�0蟺sinxcosydxdy=[-cosxsiny]=0

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Most popular questions from this chapter

Use the results of Exercises 59 and 60 to find the centers of masses of the lamin忙 in Exercises 61鈥�67.

In the following lamina, all angles are right angles and the density is constant:

Find the masses of the solids described in Exercises 53鈥�56.

The solid bounded above by the hyperboloid with equation z=x2-y2 and bounded below by the square with vertices (2, 2, 鈭�4), (2, 鈭�2, 鈭�4), (鈭�2, 鈭�2, 鈭�4), and (鈭�2, 2, 鈭�4) if the density at each point is proportional to the distance of the point from the plane with equationz = 鈭�4.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals

鈭�鈭�R(2-3x2+y3)dAWhereR={(x,y)|-3鈮�x鈮�2,3鈮�y鈮�5}

In the following lamina, all angles are right angles and the density is constant:

Use the results of Exercises 59 and 60 to find the centers of masses of the lamin忙 in Exercises 61鈥�67.

Use the lamina from Exercise 61, but assume that the density is proportional to the distance from the x-axis.
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