Mathematics - Area Under Curves Question with Solution | TestHub

Intersecting points are $x=1,4$ $$\begin{array}{rl}& \therefore \text{ Required area }={\int }_1^4\left[2\sqrt{x}-\left(\frac{2x+4}{3}\right)\right]dx\\ & ={\frac{2x^{3/2}}{3/2}|}_1^4-{\frac{2x^2}{3\times 2}|}_1^4-{\frac{4}{3}x|}_1^4\end{array}$$ $$\begin{array}{rl}& =\frac{4}{3}\left(4^{3/2}-1^{3/2}\right)-\frac{1}{3}(16-1)\left[\frac{4}{3}(4)-\frac{4}{3}\right]\\ & =\frac{4}{3}(7)-5-4=\frac{28}{3}-9=\frac{28-27}{3}=\frac{1}{3}\end{array}$$