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interesting integration:- integration of [0 to 90 deg] (sin x -cos x)/(1 - sin 2x)^0.5 dx?
the answer is coming zero by using properties of definite integrals, but it is coming 90 deg without using prop.
which answer is correct?
what do i do if a similar que comes in an exam?
PLEASE READ THE FULL QUE. AND TRY IT USING PROPERTIES OF DEFINITE INTEGRAL!
THEN THE ANSWER IS COMING ZERO!!
WHY SO?
2 Answers
- 7 years ago
Note that numerator and denominator in this expression are same.
1- sin 2x = sin2x+ cos2 x - 2 sin x cos x = (sin x-cos x)^2
There fore rest of the operations are straight forward and answer is 90 degrees or pi/2 radians.
- RameshwarLv 77 years ago
int (sinx -cosx)/(1-sin2x)^1/2
= intsinx - cosx/(sin^2x+ cos^2x-2 sinx cosx)^1/2
= int (sinx -cosx)/( sinx- cosx) dx
= x lim 0 to pi/2
= pi/2 answer
