I have already calculated the integrals. They are: f[x,y] = 0 g[x,y] = 29.5 h[x,

Question

I have already calculated the integrals. They are:

f[x,y] = 0

g[x,y] = 29.5

h[x,y] = 0

I just need help with the last part. Can someone please explain why it was no surprise that f[x,y] and h[x,y] came out the way they did? Thanks!

Top half of R ottom half of R Go with g[x,y]=y, e-x and and calculat f[x, y]dxdy glx, y]dxdy , and h[x, y]dxd y by the method of least labor on your part Look at the formulas for f[x.y] and g[x.y] and then look at the shape and position of R and explain why it was no surprise that f[x, y]dxdy andh[x, y]dxdy came out the way they did

Explanation / Answer

As we have f[x,y] and h[x,y] are odd functions their integral about the region would result in zero as we can see on putting the limits we will have an odd function whose limits will be -2 to 2 in terms of y which will lead to the result becoming zero as the integration from 0 to 2 will be same as -2 to 0 with a negative sign hence both will cancel each other giving us the result zero.

whereas we can see that g[x,y] is even function hence its result of integral is not zero.

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