Calculus Integrals problem, pls help! Find F'(x)

Question

Find F'(x)

F(x) = ∫₀^{x^3} (sin(t⁴))dt

F(x) is the integral from 0 to x³ of sin(t⁴).

Find the derivative of F(x).

Answer 1

F(x) = ∫_{(from 0 to x^3)} sin(t⁴)dt

To find F'(x), use the Chain Rule and Fundamental Theorem of Calculus as follows:

Since the lower limit is constant, replace t by x³ and then multiply by the derivative of x³

So, F'(x) = sin(x³)⁴ (x³)' = 3x²sin(x¹²)

Answer 2