Question

Region r is the base o a solid. for each x value, the cross section of the solid is taken perpendicular to the x-axis is a rectangle whose base lies in R and whose height is x. Write a definite integral that will give the volume of the solid.

Answer 1

`\int\limits_R x \, dx \, dy`

Explanation:

The z-coordinate can take any value between 0 and the value of the x-coordinate. On the other hand, the values of x and y are limited by those of the solid. We can summarize the volume of the solid with the following integral:

`\int\limits_R\int\limits_0^x {1} \, dz \, dx \, dy = \int\limits_R x \, dx \, dy`