find the average value o f over the region D:

f(x,y) = xsin(y), D is enclosed by the curves y =0, y=x^2, and x=1

Question

find the average value o f over the region D:

f(x,y) = xsin(y), D is enclosed by the curves y =0, y=x^2, and x=1

turingtest · Answer

I suppose that means you divide by the area of the region

anonymous · Answer

yeah i was given a formula that the double integral of f(x,y)DA = (area of R)(average value of f on R)

turingtest · Answer

so you already have the value of the double integral
can you find the area D (or R, or however you want to call it)?
that's calc I stuff

anonymous · Answer

hang on I'm trying to solve for the double integral

turingtest · Answer

oh I thought it was the same as the other, but it's a bit different

anonymous · Answer

yeah just sine

anonymous · Answer

is the double integral 1/2(1-sin1)

turingtest · Answer

I got just
-1/2sin1

turingtest · Answer

oh wait, you were right

anonymous · Answer

okay good you scared me :)

anonymous · Answer

okay so how do i solve for the area of R?

anonymous · Answer

integral of x^2?

turingtest · Answer

just like the good old days of calc 1

anonymous · Answer

the bounds given don't form a region though

turingtest · Answer

sure they do|dw:1332297950352:dw|$$R=\int_{0}^{1}x^2dx$$

anonymous · Answer

ahhhhh

anonymous · Answer

so area = 1/3?

turingtest · Answer

yep

anonymous · Answer

so average = 3/2(1 - sin1)

turingtest · Answer

guess so
never had to find an average value like this, but it makes sense

anonymous · Answer

awesome thank you so much!