Answer:
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
