Double integral over a general region
When the figure first loads, we see a region bounded below by , bounded above by , and bounded on the sides by the lines and . A function is also given and we wish to integrate over this region.
Click the checkbox next to to show/hide the surface . You can drag the 3D view to get a better perspective. Clicking the button "3D 2D" will also change the view. Computing the double integral tells us the volume of the solid above the bounded region and below .
First, we compute . Thus, tells us the cross-sectional area of the solid for any . Next, we integrate from to to get the volume of the iterated integral.
A note on manipulating the 3D view
If you make your own examples, you may need to change the 3D view to see your bounded region and the solid clearly.
- Dragging rotates the view.
- Shift+Drag will pan the view.
- Shift+Click will change the direction of the panning.
- Scroll wheel zooms in and out.