SATHEE: Area Question 51

Area Question 51

Question 51

Find the area of the region bounded by the $X$ -axis and the curves defined by $y = \tan x, - \frac{π}{3} \leq x \leq \frac{π}{3}$ and $y = \cot x, \frac{π}{6} \leq x \leq \frac{π}{3}$ .

$(1984, 4 M)$

Show Answer

Solution:

Given, $y = \tan x, - \frac{π}{3} \leq x \leq \frac{π}{3}$ $\cot x, \frac{π}{6} \leq x \leq \frac{π}{2}$

which could be plotted as $Y$ -axis.

$∴$ Required area $= \int_{0}^{π / 4} (\tan x) d x + \int_{π / 4}^{π / 3} (\cot x) d x$

$=[-\log |\cos x|]{0}^{\pi / 4}+[\log \sin x]{\pi / 4}^{\pi / 3}$

$= - \log \frac{1}{\sqrt{2}} - 0 + \log \frac{\sqrt{3}}{2} - \log \frac{1}{\sqrt{2}}$

$= \log \frac{\sqrt{3}}{2} - 2 \log \frac{1}{\sqrt{2}}$

$= \log \frac{\sqrt{3}}{2} - \log \frac{1}{2} = \frac{1}{2} \log_{e} 3$ sq units

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Area Question 51

Question 51

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu