Using the method of integration show that the area of triangle of base b and altitude h is `1/2bh`.

Explanation

To show that the area of a triangle with base \( b \) and height \( h \) is given by the formula \( \frac{1}{2}bh \) using integration, we can follow these steps:

### Step 1: Set Up the Coordinate System
We will place the triangle in the coordinate system. Let the vertices of the triangle be at the following coordinates:
- Vertex A at the origin: \( (0, 0) \)
- Vertex B at \( (b, 0) \) (on the x-axis)
- Vertex C at \( \left(\frac{b}{2}, h\right) \) (the top vertex)