Fundamental Theorem of Calculus Problem

[mathgirl]

Hi, I'm having trouble with the 2nd part of the question.

Suppose that 5x³ + 40 = integrate from c to x f(t)dt

a) What is f(x)?

I am pretty sure that I can use the Fundamental Theorem of Calculus. If I take the derivative of both sides, I get 15x² = f(x).

It's this question that I don't know how to even begin.

b) Find the value of c

Any help would be appreciated.

 

[daon2]

Integrate both sides of \(\displaystyle 15t^2 = f(t)\) from \(\displaystyle t=c\) to \(\displaystyle t=x\). The right-hand side becomes \(\displaystyle 5x^3+40\) (by assumption). The left-hand side?

 

[pka]

Suppose that 5x³ + 40 = integrate from c to x f(t)dt
I am pretty sure that I can use the Fundamental Theorem of Calculus. If I take the derivative of both sides, I get 15x² = f(x).

b) Find the value of c

\(\displaystyle 5{x^3} + 40 =\displaystyle \int_c^x {15{t^2}dt} = \left. {5{t^3}} \right|_c^x\) solve for c.