Find the area between the given curves on the interval x = 0 to x = 25.

Question

y=√x , y=1/2x

Answer 1

https://postimg.cc/bDP2Z05v

Worked the problem out on a virtual whiteboard and saved as an image, let me know if that link works! Seems the image is too high resolution to attach directly.

Answer 2

√x = 1/2x; x = 1/4x²; x = 0 or x = 4

Area A = ∫₀⁴(√x - 1/2x)dx + ∫₄²⁵(1/2x - √x)dx = (2/3x^3/2 - x²/4)₀⁴ + (x²/4 - 2/3x^3/2)₄²⁵ = 16/3 - 4 + 625/4 - 250/3 - 4 + 16/3 = 907/12