Question

(1 pt) If f(3)=15, f′ is continuous, and ∫53f′(t)dt=22, what is the value of f(5)?

Answer 1

When you wrote "∫53f′(t)dt=22", I'm guessing you meant to say

\[\Large \int_{3}^{5}f^{\prime}(t)dt = 22\]

right?

Answer 2

refresh the page if you get weird box symbols or question marks

Answer 3

thanks yes that's what I meant

Answer 4

I don't know how to take the derivative of f(t) to find a value for f(t)

Answer 5

by the fundamental theorem of calculus, we know that \[\Large \int_{3}^{5}f^{\prime}(t)dt = f(5) - f(3)\]

this is because the integral is essentially the antiderivative (it undoes the derivative operation)

Answer 6

you know f(3) and you know the value of the integral, so replace the two and solve for f(5)

Answer 7

some books call this idea "the net change theorem"

Answer 8

okay, that is starting to make more sense now