Question

Use the graph of f(t) = 2t − 5 on the interval [−2, 10] to write the function F(x), where f of x equals the integral from 1 to x of f of t dt.

Answer choices:
F(x) = 2x − 5
F(x) = x2 − 5x − 4
F(x) = x2 − 5x + 4
F(x) = x2 − 5x + 36

Answer 1

F(x) =

x
∫ ( 2 t - 5 ) dt =
1

x
( 2 t² / 2 - 5 t ) =
1

x
( t² - 5 t ) =
1

x² - 5 x - ( 1² - 5 ∙ 1 ) = x² - 5 x - ( 1 - 5 ) = x² - 5 x - ( - 4 ) = x² - 5 x + 4

Answer 2

nicely done, but it's clear that the graph was not necessary.