Sketch the region enclosed by the given curves. Finally, find the area of the shaded region.

Question

y=sqrt(x), y=(1/2)x, x=25

Answer 1

1/2x = x^1/2,, 1/4x² = x, x = 0, x = 4

A = ∫₀⁴(x^1/2 - 1/2x)dx + ∫₄²⁵(1/2x - x^1/2)dx = (2/3x^3/2 - 1/4x²)₀⁴ + (1/4x² - 2/3x^3/2)₄²⁵ = 16/3 - 4 + (625/4 - 250/3) - (4 - 16/3) = 8/3 + 875/12 = 907/12 = 75,58