Question

How do you do this question?

Answer 1

∫₁⁵ 2t (t² + t³) dt

Explanation:

The area is ∫ₓ₁ˣ² y dx. To parameterize, replace x₁ and x₂ with t₁ and t₂. Replace y = f(x) with y = f(t), and replace dx with (dx/dt) dt.

x = 5 + t², so dx = 2t dt.

∫₁⁵ (t² + t³) (2t dt)

∫₁⁵ 2t (t² + t³) dt