Question

CALCULUS: Given 5x^3 + 40 = int(f(t))dt with lower bound being c and upper bound being x.
-Find f(x)
-Find the value of c

Answer 1

So what you mean is\[5x^3 + 40 = \int\limits _c ^x f(t) dt\]?

Answer 2

Yes[:

Answer 3

Ok, so you should know that \[\frac{ d }{ dx }[\int\limits_c ^x f(t)dt] = f(x)\] So in order to solve for f(x) all you have to do is differentiate both sides of the equation.

Answer 4

Oh okay (our class is reviewing for a final and I totally forgot how to use the fundamental theorem after learning other topics)
That is also why these questions are pretty spread out as far as topics go.

Answer 5

I got 15x^2=f(x)

Answer 6

Is that right? or do I add c?

Answer 7

Alright, glad I can help :p. And yes, that is correct.

Answer 8

No need to add c (you didn't integrate anything)

Answer 9

So then in the second part it asks to solve for c

Answer 10

I'm stumped there :l. I'll be sure to tell you if I remember how to do that :p.

Answer 11

Oh please[: Thank you, I'll look into it on google more

Answer 12

Oh, and if you see this, quick question: What is the shortest way to do trapezoidal approximation? I remember my teacher showing us something to shorten it a bit I just can't find it anywhere in my notes. /: