calculus

posted by .

The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the x-axis. Each cross section perpendicular to the base and the x-axis is a square. Find the volume of the solid.

• calculus -

Each cross section (from x=0 to x=1) is a square of side √x.

So the total volume is the area of the square times dx, or A(x)dx

V=∫ (√x)^2dx from x=0 to 1
=∫ xdx
=[x²/2] from 0 to 1
= 1/2

Similar Questions

1. calculus

the base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line y=1-x. if cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?
2. Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
3. calculus

let R be the region bounded by the graphs of y = sin(pie times x) and y = x^3 - 4. a) find the area of R b) the horizontal line y = -2 splits the region R into parts. write but do not evaluate an integral expression for the area of …
4. Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the …
5. Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the …
6. Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the …
7. Calculus

The base of a solid is the region bounded by the parabola y^2=4x and the line x=2. Each plane section is perpendicular to the x-axis is a square. What id the volume of the square?
8. Calculus AP

Let R be the region bounded by the graphs of y=cos((pi x)/2) and y=x^2-(26/5)x+1. A. Find the area of R. B. The vertical line x=k splits the region R into two equal parts. Write, but do not solve, an equation involving integrals that …
9. calculus

The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume of …
10. Calculus

A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid

More Similar Questions