00:01
In this question, we're given that the slope of a curve is this, and the point one, two, is on the curve, and we want to find the curve equation.
00:10
If i were to draw in general a curve, y, and draw a slope, the slope will be a tangent to a point on the curve.
00:22
So at this point, the slope is actually your d, y, dx, and that is equals to your long x, the whole thing square over x.
00:32
And i can draw the point one to anywhere, just an illustration.
00:38
So to find the curve equation, we need to integrate the d, y, dx.
00:48
Applying integration sign on both sides.
00:53
When you write the integration sign, don't forget to write the dx or dy or whatever you want to integrate with respect to.
01:03
On the left side, we will have y, since when we integrate a differentiation, it will be y itself.
01:09
On the right side, we can use a couple of methods to integrate.
01:15
For this topic, we are using substitution method and an integration power rule.
01:20
So for substitution method, let u be equals to lonex.
01:29
So d u over the x is 1 over x.
01:33
D u will be 1 over x d x.
01:36
As you can see here, i can rearrange this such that this part is the u and long as is u...