Find $\displaystyle\int\dfrac{x}{\sqrt{1-x^2}}\,\mathrm{d}x$. Hence find the exact value of \(\dis

Question

Find $\displaystyle\int\dfrac{x}{\sqrt{1-x^2}}\,\mathrm{d}x$. Hence find the exact value of $\displaystyle\int_0^{1/2}\dfrac{x^3}{\sqrt{1-x^2}}\,\mathrm{d}x$.

Accepted Answer

(a) $-\sqrt{1-x^2}+C$ (b) $\dfrac{2}{3}-\dfrac{3\sqrt3}{8}$

Mixed Integration Techniques

Mixed Integration Techniques