Page:Calculus Made Easy.pdf/231

 All integration between limits requires the difference between two values to be thus found. Also note that, in making the subtraction the added constant $$C$$ has disappeared.

Examples

(1) To familiarize ourselves with the process, let us take a case of which we know the answer beforehand. Let us find the area of the triangle (Fig. 53), which



has base $$x=12$$ and height $$y=4$$. We know beforehand, from obvious mensuration, that the answer will come $$24$$.

Now, here we have as the “curve” a sloping line for which the equation is

The area in question will be

Integrating $$\dfrac{x}{3}\, dx$$ (p. 194), and putting down the