Find the area of the region bounded by the lines $x-y=1 $ and $x$-axis,$x=2$ and $x=4$

Answer 1

Toolbox:

• Area bounded by the curve $t=f(x),$ the x-axis and the ordinates $x=a,x=b$ is $\int \limits_a^b f(x) dx $ or $ \int \limits _a^b y dx $
• If the curve lies below the x-axis for $a \leq x \leq b,$ then the area is $\int \limits_a^b (-y) dx=\int \limits_a^b (-f(x))dx$

http://clay6.com/mpaimg/tn%207.4%20(i).JPG

Area bounded by the line $x-y=1$ and $x-axis, x=2,x=4$

$x-y=1=>y=x-1$

$A=\int \limits_2^4 y dx$

$\quad= \int \limits_2^4 (x-1) dx$

$\quad= \large\frac{x^2}{2}$$-x \bigg]_2^4$

$\quad= (8-4)-(2-2)$

$\quad= 4\;sq \;units$