Mathematics - Area Under Curves Question with Solution | TestHub

The given curve passes through $(1,2)$. $\therefore 2=a+b$ According to the given condition, ${\int }_0^4(a\sqrt{x}+bx)dx=8$ ...(i) $\Rightarrow \frac{2\mathrm{a}}{3}{\left[x^{3/2}\right]}_0^4+\frac{\mathrm{b}}{2}{\left[x^2\right]}_0^4=8\Rightarrow \frac{2\mathrm{a}}{3}\cdot 8+8\mathrm{b}=8$ $\Rightarrow 2a+3b=3$ ...(ii) From (i) and (ii), we get $\mathrm{a}=3,\mathrm{b}=-1$