FUNDAMENTAL THM OF CALCULUS

Question

Let 𝐹(𝑥)=lower limit x, upper limit -2 ∫−6cos(t^2)𝑑𝑡.Use the Fundamental Theorem of Calculus to find 𝐹′(𝑥).

Answer 1

F(x) = -∫_x^-26cos(t²)dt = ∫_-2^x6cos(t²)dt because ∫_a^b = -∫_b^a

F'(x) = 6cos(x²) because by FTC d/dx∫_a^x g(t)dt = g(x)