Inverse Calculus

Calculus Level 3

∫ − π 3 π cot ⁡ − 1 ( cot ⁡ x ) d x = ? \large \displaystyle \int_{-\pi}^{3 \pi} \cot^{-1}(\cot x) \, dx= \ ?

Note: The range of cot ⁡ − 1 \cot^{-1} is ( 0 , π ) (0, \pi ) .

2 π 2 2 \pi^2 9 π 2 9 \pi^2 3 π 2 3 \pi^2 16 π 2 16 \pi^2

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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4 solutions

Akshay Sharma
Dec 10, 2015

replacing 'x' by (2pi-x) and adding both the integrand we get answer 2[pi]^2

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Sorry but I didn't understood how. ? Could you show how it's done ?

Anurag Pandey - 4 years, 2 months ago

Using graph ,it is just the area of 4 congruent triangle. All the triangles are right angled

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Rohith M.Athreya
Feb 1, 2017

integral over an entire period is the same so it is

4 ∫ 0 π x d x 4\int_{0}^{\pi}xdx

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain, please ?

Aditya Sky - 4 years, 1 month ago
Mini Gupta
Jan 7, 2017

use graph of arccot(cotx)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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