Question

Consider the region bounded by

Answer 1

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