Use the graph of f(t) = 2t + 1 on the interval [-1, 4] to write the function F(x), where f of x equals the integral from 2 to x of f of t dt

Question

 

Use the graph of f(t) = 2t + 1 on the interval [-1, 4] to write the function F(x), where  

A.) F(x) = x2 + 3x

B.) F(x) = 2x + 1

C.) F(x) = x2 + x - 20

D.) F(x) = x2 + x - 6

Answer 1

f(x) = 2t +1

F(x)= t^2 + t + c

F(-1) = 1-1+c = c

F(4) =16+4+ c =20+c

F(-1)-F(4) = -20

D) F(x) = x^2 +x -6

F(2) = 2^2+2 +c = 6+c