Definite Integral- Find F

Question

Given F(x)= {symbol} upper value x^2 and lower value 1 square root 2t+2 dt

Answer 1

F9x)= ∫₁^{x^2}√(2t + 2)dt = √2(t + 1)^3/2·2/3₁^{x^2} = (2√2/3)(x² + 1)^3/2 - 8/3

Answer 2

F(x) = ∫_{(from 1 to x}2₎ √(2t+2)dt

F(1) = ∫_{(from 1 to 1)} √(2t+2)dt = 0

F'(x) = √(2x²+2) (x²)' = 2x√(2x²+2)

F'(1) = 2√4 = 4