Question

The area bounded by the curve y=tanx, x=−π/4,x=π/3y=tan⁡xx=−π4,x=π3, and x-axis ?

• A. $\frac{\ln 2}{2}$
• B. $\ln 2$
• C. $\frac{2}{3}\ln 2$
• D. $\frac{3}{2}\ln 2$

Answer 1

The correct option is A $\frac{\ln 2}{2}$

Area $={\int }_{-\pi /4}^{\pi /3}\tan xdx$

$=[ln|\sec x|{]}_{-\pi /4}^{\pi /3}$

$=ln|\sec \pi /3|-ln|\sec (-\pi /4)|$

$=ln2-ln\sqrt{2}$

$=ln2-\frac{1}{2}ln2$

$=\frac{ln2}{2}$