Find the arc length of the graph of the given equation from A to B. y = 6x^2/3 +1; А(-1,7), В(-8,25)

Answer 1

arc length = S(sqr(1- (f'(x))^2)dx evaluated from -1 to -8

= integral of ]sqr(1-16x^(4/3])dx from -1 to -8

use integral tables or an online integral calculator

or

use u substitution u =x^(1/3), du = (1/3x)dx, dx = 3x(2/3)du, u^2 = x^(2/3)

to get integral of u^2(sqr(1-16u^2)du

then use trig substitution, u =sinv/4

then hyperbolic substitution

then use product to sum formulas

it gets messy

Answer 2

desmos.com/calculator/cwxl8hdq3d