How can I find the area of the region of y=radicalx, y=x^2, and x=2?

Question

Sketch the region enclosed by the given curves. Find the area of the region. y=radicalx, y=x^2, and x=2.

Answer 1

The two curves cross at x = 1, so we have x² = f₂ and sqrt(x) = f₁ with f₂ ≥ f₁ for x≥1

So you need to integrate from x = 1 to x =2 of (f₂-f₁)dx which is just a difference of integrable power functions.