edgy token
Hi, good day. We were given a practice exercises for our upcoming exam. Our topic is about multiple integration. I have here a triple integral. Can someone check my work for this? Huhuhuhu I am not really sure about my process. I just want to ask help to check my work in converting the original equation using polar coordinates. #1020426321261756536
long cloud
Hi, good day. We were given a practice exercises for our upcoming exam. Our topi...
Spherical coordinates would be better, I think.
dxdydz = r^2 sin(θ)drdθdφ
The new limits are:
0 < r < 2
0 < θ < π
0 < φ < π
The expression under the integral becomes r^3 sin(θ)^2 cos(φ)drdθdφ. From this, you can now easily see what the integral evaluates to.
long cloud
That is correct.
long cloud
But both of them will give same answer right?
Of course. Doesn't matter which methods you use, as long as you don't make a mistake, the answer will be the same.
It's just that I can see that these limits define a region inside a half-sphere, so spherical coordinates came up to mind.
edgy token
Okayy okayy thank you for thiss!! I chose polar coordinates because I am yet to study spherical coordinates hehehe
long cloud
Ah, I see. Well, it is the right approach, still!
I do recommend learning about spherical coordinates, though.