Volume using Cross Sections (Calculus):
The base of a solid is bounded by , the x-axis, and the y-axis. Cross sections that are perpendicular to the x-axis are isosceles right triangles with the right angle on the x-axis. (Legs perpendicular to the x-axis). Find the volume.

Question

Volume using Cross Sections (Calculus):
The base of a solid is bounded by  , the x-axis, and the y-axis. Cross sections that are perpendicular to the x-axis are isosceles right triangles with the right angle on the x-axis.  (Legs perpendicular to the x-axis).  Find the volume.

mathmale · Answer

Your base has not yet been completely bounded.  The x- and y-axis do serve as boundaries, but there must be at least one more boundary.  You might want to sketch the base as a starting point.

holsteremission · Answer

Looks like whatever the OP copied didn't get carried over correctly.

Let's assume the bounded region is in the first quadrant, so we're dealing with a region like this:
|dw:1479917726619:dw|
Then the solid we're concerned with looks like this:
|dw:1479917856955:dw|
The volume is the sum of an infinite number of triangles' areas whose legs' lengths are determined by the value of $f(x)$ at a particular $x$, with each triangle having area $\dfrac{1}{2}f(x)^2$ (as both base and height are given by $f(x)$). In the form of an integral, you have
$$V=\frac{1}{2}\int_0^tf(x)^2\,\mathrm dx$$