The area of the region bounded by the line y= | vedclass

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(C) The line $y=2x+1$ intersects the $X$-axis at $x=-\frac{1}{2}$.For $x \in [-1, -\frac{1}{2}]$,$y \le 0$,and for $x \in [-\frac{1}{2}, 1]$,$y \ge 0$

Vedclass · Accepted Answer

$\frac{5}{2}$

Vedclass · Answer

(C) The line $y=2x+1$ intersects the $X$-axis at $x=-\frac{1}{2}$.For $x \in [-1, -\frac{1}{2}]$,$y \le 0$,and for $x \in [-\frac{1}{2}, 1]$,$y \ge 0$.The required area is given by:$	ext{Area} = \int_{-1}^{1} |y| dx = \int_{-1}^{-1/2} -(2x+1) dx + \int_{-1/2}^{1} (2x+1) dx$$= -[x^2+x]_{-1}^{-1/2} + [x^2+x]_{-1/2}^{1}$$= -[(\frac{1}{4} - \frac{1}{2}) - (1 - 1)] + [(1+1) - (\frac{1}{4} - \frac{1}{2})]$$= -[-\frac{1}{4}] + [2 - (-\frac{1}{4})]$$= \frac{1}{4} + 2 + \frac{1}{4} = \frac{1}{2} + 2 = \frac{5}{2} 	ext{ sq units}$.

The area of the region bounded by the line $y=2x+1$,the $X$-axis,and the ordinates $x=-1$ and $x=1$ is

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