Question

The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is

• A. $\frac{7}{2}\mathrm{square}\mathrm{units}$
• B. $\frac{9}{2}\mathrm{square}\mathrm{units}$
• C. $\frac{11}{2}\mathrm{square}\mathrm{units}$
• D. $\frac{13}{2}\mathrm{square}\mathrm{units}$

Answer 1

The correct option is A $\frac{7}{2}\mathrm{square}\mathrm{units}$

Area under the curve is given by
$={\int }_2^{3}y\mathrm{dx}={\int }_2^3\left(x+1\right)\mathrm{dx}={\left(\frac{x^2}{2}+x\right]}_2^3=\left(\frac{9}{2}+3-2-2\right)=\frac{7}{2}\mathrm{square}\mathrm{units}$