The curve $y=\tan x$ meets the line $y=-\dfrac{2\sqrt3}{\pi}x+\dfrac{2}{\sqrt3}$ at $A$, where

Question

The curve $y=\tan x$ meets the line $y=-\dfrac{2\sqrt3}{\pi}x+\dfrac{2}{\sqrt3}$ at $A$, where the $x$-coordinate of $A$ is $\dfrac{\pi}{6}$. The line meets the positive $x$-axis at $B$. Find the coordinates of $B$.[2] Find the exact area of the shaded region bounded by the curve, the line and the $x$-axis.[5]

Accepted Answer

(i) $B=\left(\dfrac{\pi}{3},0\right)$ (ii) $\ln\left(\dfrac2{\sqrt3}\right)+\dfrac{\pi\sqrt3}{36}\text{ units}^2$

Tangent curve and a descending line

Tangent curve and a descending line

Video Solution:

Solution:

Solution locked