Use the graph of f(t) = 2t + 4 on the interval [-4, 6] 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 + 4 on the interval [-4, 6] to write the function F(x), where  

A	F(x) = x2 + 6x
B	F(x) = x2 + 4x - 12
C	F(x) = x2 + 4x - 8
D	F(x) = x2 + 8x - 20

Answer 1

Answer is

B	F(x) = x2 + 4x - 12

The fundamental theorem of calculus part 1

d/dx [ ∫₂^x f(t) dt ] = f(x)

F(x) = ∫₂^x ( 2t+4) dt

= 2 t² /2 + 4t Ι^x₂

= t² + 4t Ι^x₂

= ( x² + 4 x ) - ( 2² + 4* 2)

= x² + 4 x- 12