00:01
In this question, we're given the slope to a curve is this, and the curve passes through the point to 1.
00:07
Our job is to find this curve.
00:09
Now, let's just draw a general curve.
00:13
This is y.
00:14
Now, a slope to the curve will look like this.
00:16
It's actually a tangent to a point on the curve.
00:20
Now, at this point, the slope is the dy over dx.
00:24
So this is the dydx.
00:26
To find the equation on the curve, we need to integrate this dydx.
00:30
So let's take a look.
00:35
Dydx is this slope expression here.
00:43
Now applying integration sign on both sides.
00:47
Now it's important to know that when you write the integration sign, you must write with respect to which variable, dx or dy or whatever variable you're working with.
00:58
Now on the left side, when we integrate a differentiation, you'll just get back y itself.
01:04
On the right side, there are a couple of methods to integrate.
01:07
For this topic, we are using substitution method and an integration power rule...