Getting the image of integration

[farmd684]

How can i get the image of a integral. Say i have a integral function like this
$$\int_{\pi/2}^{\pi} \int_{0}^{2} r\sqrt{4-r^2} drd\theta$$

Now i want to see what volume the integral giving me. Which software i have to use for this purpose.

Thanks

 

[slider142]

For this particular integral, you can use any software that plots functions of two variables. In this case, I am assuming the third variable is z, as in cylindrical coordinates, and the integral is evaluating the volume under this surface:

A lot of free software offers this capability, including GraphCalc and Maxima. Note that you can replace r with $\sqrt{x^2+y^2}$ in order to enter the equation as z = f(x, y) if necessary.

 

[HallsofIvy]

How can i get the image of a integral. Say i have a integral function like this
$$\int_{\pi/2}^{\pi} \int_{0}^{2} r\sqrt{4-r^2} drd\theta$$

Now i want to see what volume the integral giving me. Which software i have to use for this purpose.

Thanks

That's in polar coordinates with $\theta$ going from $\pi/2$ to $\pi$- in Cartesian coordinates, that is the second quadrant. r ranges from 0 to 2 so, within the second quadrant, we are within a circle of radius 2. Finally, the upper boundary is $r\sqrt{4- r^2}$ we can put that in Cartesian Coordinates by setting $= \sqrt{x^2+ y^2}$ so that $z= r\sqrt{4- r^2}= \sqrt[x^2+ y^2}\sqrt{4- x^2- y^2}$. I doubt that is any 'standard' figure.