Question

Suppose that the integral of x-1 of f(t) dt = 5x^2 + 7x -3. Find f(x)

Answer 1

\[\int\limits_{x}^{1} f(t) dt = 5x^2 + 7x - 3\]

is that written correctly ?

Answer 2

x is on the top

Answer 3

if so, use the fact that

\[\int\limits_{b}^{a} f(x) dx = -\int\limits_{a}^{b} f(x) dx\]

and the fundamental theorem of calculus

\[d/dx \int\limits_{a}^{x} f(t) dt = f(x)\]

Answer 4

ah, in that case just use the fundamental theorem of calculus

Answer 5

i.e., take the derivative of both sides with respect to x

Answer 6

quick question, when writing the integral out, a should come before b? like how I put x-1, should it have been x-a?

Answer 7

i read it as "from x to 1", so to be clear in writing it out you could say "from a to b"

Answer 8

or more precisely, "from [lower limit] to [upper limit]"

Answer 9

ok thanks! I was confused about that as well

Answer 10

what you take the derivative with respect to x on both sides, what do you end up with ?