Logarithm of Sine!

Calculus Level 4

Find the value if the integral :

A = ∫ ln (sin X) dX , from X = π to 0.

Find the Value of [1000*A] , where [Z] represents Greatest integer less than or equal to Z.


The answer is 2177.

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1 solution

Lu Chee Ket
Feb 10, 2015

From 0 to Pi/2, this standard integral is equals to - (Pi/ 2) Ln 2.

From 0 to Pi, symmetry of Sin x tells a doubled value of - Pi Ln 2 which can be confirmed by numerical integration.

From Pi to 0 is therefore Pi Ln 2.

[1000 * 2.1775860903036021305006888982376] = 2177

Mod: is this answer valid?

E Koh - 1 year, 5 months ago

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