Question

Use the graph of f(t) = 2t + 2 on the interval [-1, 4] to write the function F(x), where f(x) = x∫-1 f(t) dt
a. F(x) = x^2 + 3x
b. F(x) = x^2 + 2x - 12 (my answer)
c. F(x) = x^2 + 2x - 3
d. F(x) = x^2 + 4x - 8

Answer 1

sorry the integral denotation is x∫1 (not x∫-1)

Answer 2

integral is t^2 + 2 t + constant
so at t = x minus at t = 1
x^2 + 2 x + c - 1^2 -2 - c
= x^2 + 2 x - 3

Answer 3

Thank you!