# Thread: Finding the equation of the curve

1. ## Finding the equation of the curve

Hello everyone,
Here is a question ive been trying to solve for hours.

* A curve passes through the point (25,3) and is such that dy/dx=1/2√x.
Find the equation of the curve

Rob

2. Originally Posted by Oasis1993
Hello everyone,
Here is a question ive been trying to solve for hours.

* A curve passes through the point (25,3) and is such that dy/dx=1/2√x.
Find the equation of the curve

Rob
$\displaystyle \frac{dy}{dx}=\frac{1}{2}\sqrt{x}$

Integrate this :

$\displaystyle y=\int{\frac{1}{2}\sqrt{x}}$

Then substitute 25 into x and 3 into y to find the constant .

$\displaystyle \frac{dy}{dx}=\frac{1}{2}\sqrt{x}$

Integrate this :

$\displaystyle y=\int{\frac{1}{2}\sqrt{x}}$

Then substitute 25 into x and 3 into y to find the constant .
could you please integrate it for me?

I have big trouble integrating numbers which have a square root.

4. Originally Posted by Oasis1993
could you please integrate it for me?

First of all , bring the constant out .

Then if you integrate $\displaystyle x^{\frac{1}{2}}$ , it becomes

$\displaystyle \frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}$

Then don forget the plus c .. since its an indefinite integral

5. Originally Posted by Oasis1993
I have big trouble integrating numbers which have a square root.
You're expected to realise that $\displaystyle \sqrt{x} = x^{1/2}$ and then use the usual rule for integrating $\displaystyle x^n$.