# Thread: Equation of a curve

1. ## Equation of a curve

A curve has gradient e(power 4x)+e(power -x) at the point (X,Y). Given that the curve passes through the point (0,3), find the equation of the curve.

Plz Help!

2. ## Re: Equation of a curve

What ideas have you had so far?

3. ## Re: Equation of a curve

no idea at all!

4. ## Re: Equation of a curve

Well, you're given the derivative of a function. You'd like to get the function itself. How can you do that?

5. ## Re: Equation of a curve

The gradient function is $\displaystyle e^{4x} + e^{-x}$.

If $\displaystyle \frac{dy}{dx} = e^{4x} + e^{-x}$, then what is $\displaystyle y$? In other words, how do you undo taking a derivative?

Dunno!

7. ## Re: Equation of a curve

Have you studied integration at all?

8. ## Re: Equation of a curve

Yes, but did not do any of my homeworks..!!! So i forgot everything...!!

9. ## Re: Equation of a curve

The integration in question uses $\int e^{ax} = \dfrac{1}{a}e^{ax} +C$. If you don't know why this is the case you'll need to use a textbook or ask your teacher for some more tuition and/or examples on integration

10. ## Re: Equation of a curve

Well, the most basic thing about integration is that it is, up to a constant, the inverse of differentiation. Let's say I take the function f(x) = sin(x), and I differentiate it to obtain f'(x) = cos(x). Well now, I can integrate it to get back to my original function:

$\int\cos(x)\,dx=\sin(x)+C.$

Notice the constant there. So use the antiderivative that e^(i*pi) just gave you, plus this fact, and then use the constant of integration to make your curve go through the desired point. Does that make sense?

11. ## Re: Equation of a curve

Originally Posted by Ackbeet
Have you studied integration at all?
Which you might also know as antidifferentiation...

12. ## Re: Equation of a curve

Originally Posted by Khevish
Yes, but did not do any of my homeworks..!!! So i forgot everything...!!
As you brew, so shall you drink ....

Surely the first thing you do is go back, review your class notes and textbook and then do some of the work that you admit to not having done yet.