Question

Evaluate ${\int }_0^{1/2}\frac{dx}{(4+9x^2)}.$

Answer 1

${\int }_0^{1/2}\frac{dx}{[4+(3x{)}^2]}={\int }_0^{1/2}\frac{dx}{4[1+(\frac{3x}{2}{)}^2]}=\frac{1}{4}ta{n}^{-1}\frac{\left(\frac{3x}{2}\right)}{3/2}{|}_0^{1/2}$

$=\frac{1}{6}ta{n}^{-1}\frac{3x}{2}{|}_0^{1/2}$

$=\frac{1}{6}ta{n}^{-1}3/4$