Question

INSTANT FAN AND MEDAL:
Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. g(x) = x^2 Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares.

Answer 1

Have you tried google?

Answer 2

no, why?

Answer 3

Important that you sketch this scenario. Able to do that in Draw (below)?

Answer 4

Once you've sketched the area in question, you'll see that y=x^2 and y=-ln x intersect at roughly halfway between x=0 and x=1. The length of each square cross section would be the distance separating the two curves at any given y value. The smallest y value is 0 and the largest (between 0 and 1) needs to be calculated, perhaps via Newton's Method.

Each "slice" of this solid will have thickness dy.

Once you've shared your sketch, I'd be happy to continue discussing this problem.

Answer 5

@mathmale thanks sorry for late response had a family emergency