Calculus

Application of Integrals

Medium

core

The area (in sq. units) of the region bounded by the line $2y=3x+6$ , x-axis and the ordinates x=-3 and x=1 is:

$\frac{15}{2}$

$\frac{9}{2}$

$\frac{15}{4}$

$\frac{9}{4}$

✅ Correct Option: 1

The line meets the x-axis at $x=-2$ , so the region splits there.

On $[-3,-2]$ the line is below the axis: area $=\left|\int_{-3}^{-2}\frac{3x+6}{2}dx\right|=\frac34$ .

On $[-2,1]$ it is above: $\int_{-2}^{1}\frac{3x+6}{2}dx=\frac{27}{4}$ .

Total $=\frac34+\frac{27}{4}=\frac{15}{2}$ .

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