Area b/w Curves
Find the area between the curves y=0 and y=x3+6 from x=0 to x=3.
What is 27?
A region is bounded by y=x, x=4, and y=0. It is revolved around the x-axis. Find the volume.
What is 64𝝅/3?
Find the volume of a solid whose base is bounded by y=√(25-x2) and y=0 from x=-5 to x=5. The cross sections perpendicular to the x-axis are squares.
What is 500/3?
Solve. y'=x2/y
What is √(2x2/3+c)?
Find the area between the curves y=x and y=3x3.
What is 1/4?
Find the volume of the solid of revolution generated by rotating the region between the graph of y=x1/2 and the x-axis over the interval [1,4] around the x-axis.
What is 15𝝅/2?
Find the volume of a solid whose base is bounded by y=√x, y=0, and x=4. The cross sections perpendicular to the x-axis are rectangles with a height of three times the base.
What is 24?
Find the particular solution to y'=2/y using the initial condition f(1/2)=8.
What is y =√(4x+62)?
Find the area between the curves y=x2-3 and y=1.
What is 32/3?
Find the volume of the solid of revolution generated by rotating the region between the graph of y=x1/2 and the x-axis over the interval [1,4] around the x-axis.
What is 8𝝅/15?
Find the volume of a solid whose base is bounded by y=x+1 and y=x2-1. The cross sections perpendicular to the x-axis are rectangles of height 5.
What is 45/2?
Find the particular solution to y'=2xy using the initial condition f(0)=3.
What is y=3e^x2?
Find the area between the curves y=x2+2 and y=2x+5.
What is 36?
The region bounded by y=x3, x=1, and the y-axis between y=1 and y=8 is revolved about the y-axis. Find the volume.
What is 58𝝅/5?
Find the volume of a solid whose base is bounded by y=√s and y=x/3, from y=0 to y=3. The cross sections perpendicular to the y-axis are rectangles of height 6.
What is 27?
Find the particular solution to y'=(e^-y)(2x-4) using the initial condition f(5)=0.
What is y=ln(x^2-4x-4)?
Find the area between the curves x=y2-y-6 and x=2y+4.
What is 343/6?
A region is bounded by y=(3x+1)^(1/3), x=3, and x=0. It is revolved around the x-axis. Find the volume.
What is (𝝅/5)(10^(5/3)-1)?
Find the volume of a solid whose base is bounded by y=4-x2 and the x-axis from x=-2 to x=2. The cross sections perpendicular to the x-axis are semi-circles.
What is 64𝝅/15?
Find the particular solution to y' = 3x2/2y+1 using the initial condition y(0)=2.
What is y= (-1+√(4x^3+25))/2?