A solid lies between planes perpendicular to the x-axis at xequals 0 and xequals 15. The cross-sections perpendicular to the axis on the interval 0less than or equals xless than or equals15 are squares with diagonals that run from the parabola y equals negative 2 StartRoot x EndRoot to the parabola y equals 2 StartRoot x EndRoot . Find the volume of the solid.

1800units³

Step-by-step explanation:

The formula to calculate the volume of the solid is expressed as;

∫A(x) dx within the range [0, 15]

A(x) will be the area of the squares with diagonals that run from the parabola y1 = -2√x to the parabola y2 = 2√x

Side length = L

Area A(x) = L²

L = y2-y1

A(x) = (y2-y1)²

A(x) = [2√x-(-2√x)]²

A(x) = [2√x+2√x]²

A(x) = (4√x)²

A(x) = 16x

Substitute A(x) = 16x into the formula to calculate the volume of the solid above will give;

∫16xdx within the range [0, 15]

On integrating:

= ∫16xdx

= 16∫xdx

= 16(x^{1+1}/(1+1)

= 16(x^2)/(2)

= 8x²+C

Substitute the limits [0,15] into the resulting expression

Lower limit occur at x = 0

= 8(0)²

= 8×0

= 0

Upper limit occurs at x= 15

= 8(15)²

= 8×225

= 1800

The volume of the solid will be the difference between the upper limit and the lower limit

Volume of the solid = 1800-0

Volume of the solid = 1800units³

can i get the link to the assignment?

step-by-step explanation:

the forst and 3rd

step-by-step explanation: