Find F as a function of x and evaluate it at x = 2, x = 5 and x = 9. F(x) = x 2 (t3 + 8t − 4) dt

Question

Find F as a function of x and evaluate it at x = 2, x = 5 and x = 9.

F(x) = x

2 (t3 + 8t − 4) dt

F(5) =

Answer 1

F(x) = ∫_{(from 2 to x))} (t³ + 8t - 4)dt

F(2) = ∫_{(from 2 to 2)} (t³ + 8t - 4)dt = 0

F(5) = ∫_{(from 2 to 5)} (t³ + 8t - 4)dt = [(1/4)t⁴ + 4t² - 4t]_{(from 2 to 5)} = (625/4 + 100 - 20) - (4 + 16 - 8)

Find F(9) in a similar manner.