Question

Using definite integration, fine the area of the triangle with vertices at $A(1,1)$, $B(1,1)$ and $C(4,1)$.

Answer 1

REF.Image.

A (1 , 1) B (4 , 4) C (4 , 1)

Line AB : x = y

Line BC : y = 1

Area $=\int y_{1}dx-\int y_{2}dx$

$={\int }_1^{4}xdx-{\int }_1^{4}1dx.$

$\Rightarrow [\frac{x^2}{2}-x{]}_1^4=(\frac{16}{2}-4)-(\frac{1}{2}-1)$

$=9/2$