What is the volume of the region bounded by y=sqrt(cosx) from [-pi/2, pi/2] and whose cross sections are isosceles right triangles with horizontal leg in the xy -plane.
I assume the cross sections are taken perpendicular to the x-axis? This seems more likely than relative to the y-axis as far as easiness of calculation goes.
The base of each triangle is then determined by the distance between [tex]\sqrt{\cos x}[/tex] and the x-axis, or simply [tex]\sqrt{\cos x}[/tex]. Because it's a right triangle, you know the legs' lengths occur in a 1:1 ratio. Since each triangular cross section has one of its legs as its base, the heights must be the same as their bases.
