I am a student. I was recently taught about application of integrals
case 1:
When curve $y=f(X)$ lies above the $X$ axis
the area under curve is calculated using integration
- $\text{area} = \int y\,\text dx$ with some limits
Similarly:
case 2:
When the curve $y=f(X)$ lies below the $X$ axis
The area under curve is calculated using integration
- $\text{area} = \int -y\,\text dx$ with some limits
So my question here is :
If we have to calculate area bounded by parabola $y^2= 16x$ and its latus rectum we find the area above the $X$ axis by using the equation and multiply it by 2
The equation here represents the parabola and integrating the equation with proper limits should give the area of all of the required region
That is region above and below the $X$ axis
Then why we multiply the result of integration by 2.