Bounded regions

Question

Sketch the region bounded by the given curves. Decide whether to integrate with respect to x or y. Then find the are of the region.

2y = 4sqrtx, y= 5, and 2y +2x = 6. Use desmos or something.

Answer 1

2√x = 3 - x; x + 2√x - 3 = 0; x = 1; y = 2; x = 3 - y; x = y²/4; 2 ≤ y ≤ 5.

Area A = ∫₂⁵(y²/4 - 3 + y)dy = (y³/12 - 3y + y²/2)₂⁵ = ((125/12 - 15 + 25/2) - (8/12 - 6 + 2) = 11.25