Question

Find the exact length of the curve.
x = 1 + 9^t2, y = 7 + 6^t3, 0 ≤ t ≤ 2

Answer 1

oops made a mistake when typing the problem

Find the exact length of the curve.
x = 1 + 9t^2, y = 7 + 6t^3, 0 ≤ t ≤ 2

Answer 2

s = ∫[0,2] √((18t)^2 + (18t^2)^2) dt
= ∫[0,2] 18t√(1+t^2) dt = 6(5√5 - 1)