Question Number 20385 by tammi last updated on 26/Aug/17
$$\int\sqrt{\mathrm{16}−\mathrm{9}{x}^{\mathrm{2}} {dx}} \\ $$
Answered by ajfour last updated on 26/Aug/17
$$=\mathrm{3}\int\sqrt{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{2}} −{x}^{\mathrm{2}} }\:{dx} \\ $$$$=\frac{\mathrm{3}{x}}{\mathrm{2}}\sqrt{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{2}} −{x}^{\mathrm{2}} }+\frac{\mathrm{3}×\mathrm{16}}{\mathrm{2}×\mathrm{9}}\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{3}{x}}{\mathrm{4}}\right)−{C} \\ $$$$=\frac{{x}}{\mathrm{2}}\sqrt{\mathrm{16}−\mathrm{9}{x}^{\mathrm{2}} }+\frac{\mathrm{8}}{\mathrm{3}}\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{3}{x}}{\mathrm{4}}\right)+{C}\:. \\ $$