To find the length of the curve defined by y = 5x^3+9x from the point (-3,-162) to the point (1,14), you’d have to compute the integral [a,b] f(x)dx

Question

where
a =
b =
f(x) =

Answer 1

a
L = ∫ [ sqrt 1 + ( y´ )^ 2 ] dx
b

In this case:

y´= 3 * 5 * x ^ 2 + 9 = 15 x ^ 2 + 9

1 + ( y´ )^ 2 = 1 + ( 15 x ^ 2 + 9 ) ^ 2

a = - 3

b = 1

f(x) = sqroot [ 1 + ( 15 x ^ 2 + 9 ) ^ 2 ]