# Equation of a curve

• Jun 24th 2011, 09:35 AM
Khevish
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!
• Jun 24th 2011, 09:40 AM
Ackbeet
Re: Equation of a curve
What ideas have you had so far?
• Jun 24th 2011, 09:45 AM
Khevish
Re: Equation of a curve
no idea at all!(Crying)
• Jun 24th 2011, 09:46 AM
Ackbeet
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?
• Jun 24th 2011, 09:47 AM
Prove It
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?
• Jun 24th 2011, 09:50 AM
Khevish
Re: Equation of a curve
Dunno! (Rain)
• Jun 24th 2011, 09:52 AM
Ackbeet
Re: Equation of a curve
Have you studied integration at all?
• Jun 24th 2011, 09:55 AM
Khevish
Re: Equation of a curve
Yes, but did not do any of my homeworks..!!! So i forgot everything...!!
• Jun 24th 2011, 09:57 AM
e^(i*pi)
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
• Jun 24th 2011, 09:58 AM
Ackbeet
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?
• Jun 24th 2011, 10:01 AM
Prove It
Re: Equation of a curve
Quote:

Originally Posted by Ackbeet
Have you studied integration at all?

Which you might also know as antidifferentiation...
• Jun 26th 2011, 01:18 PM
mr fantastic
Re: Equation of a curve
Quote:

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.