#differential strip

[mathproblemz]

What is the area of this region in the first quadrant ❓ #math

What is the area of the region in the first quadrant that is bounded by:

➡️ the line y = 1

➡️ the curve x = y³⁄²

➡️ and the y-axis

(A) 2/5

(B) 3/5

(C) 2/3

(D) 1

SOLUTION:

Define a differential strip with length (x - 0) and height dy.

∫ dA = ∫₀¹ x·dy = ∫₀¹ y³⁄²dy = (y⁵⁄² ÷ 5/2) |₀¹ = 2/5

THE CORRECT ANSWER IS: (A)