Consider the region bounded by
x2 + y2 = 64 with x ≥ 0, and y ≥ 0
. A solid is created so that the given region is its base and cross-sections perpendicular to the x-axis are squares. Set up a Riemann sum and then a definite integral needed to find the volume of the solid.

The equation is a circle centered at the origin with radius 8 (sqrt(64))
Therefore, the bounded region is just a quarter circle in the first quadrant.

Riemann Sum: ∑⁸ₓ₋₋₀(y²)Δx=∑⁸ₓ₋₋₀(64-x²)Δx

Definite Integral: ∫₀⁸(y²)dx=∫₀⁸(64-x²)dx

Answer Link

Consider the region bounded by x2 + y2 = 64 with x ≥ 0, and y ≥ 0 . A solid is created so that the given region is its base and cross-sections perpendicular to the x-axis are squares. Set up a Riemann sum and then a definite integral needed to find the volume of the solid.

Respuesta :

Otras preguntas

Consider the region bounded by
x2 + y2 = 64 with x ≥ 0, and y ≥ 0
. A solid is created so that the given region is its base and cross-sections perpendicular to the x-axis are squares. Set up a Riemann sum and then a definite integral needed to find the volume of the solid.