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Chapter 5: Q39P (page 248)

鈭�y=23鈭�z=12鈭�x=y+z2y+z6ydxdzdy

Short Answer

Expert verified

The solution for the given integral is 70.

Step by step solution

01

Definition of integration

Integration is a way of finding the whole by adding or summing the parts.

02

Given Integral

The integral鈭�y=23鈭�z=12鈭�x=y+z2y+z6ydxdzdy.

To find the value for the given integral.

03

Finding the integral value

Integrate the given value,

l=鈭�-236ydy鈭�12dz鈭�y+z2y+2dx=鈭�-236ydy鈭�12dz2y+z-y-z

04

Further Integrating

Now,

l=鈭�-236ydy鈭�12ydz=鈭�-236y2dy脳1=2y3-23=70

Therefore, the required solution for the given integral is 70.

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Most popular questions from this chapter

鈭�1+""a"2x2dx=x21+""a"2x2+12asinh-1a2+b2

Under the surface z = 1 /(y+2) , and over the area bounded by and y=x y2+x=2.

Find theJacobian鈭�(x,y)/鈭�(u,y)of the given transformations from variables x,yto variables u,v:

y=asinhusinv,x=acoshucosv,(uandvarecalledellipticcylindercoordinates)

Question: A partially silvered mirror covers the square area with vertices at (卤1,卤1) . The fraction of incident light which it reflects at (x, y) is(x-y)24. Assuming a uniform intensity of incident light, find the fraction reflected.

In the problems of this section, set up and evaluate the integrals by hand and check your results by computer.

鈭�x-04鈭�y-0x/2y-dy-dx
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