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sinx.log(sinx)dx=log2-1 Limit of integration:0 to pi/2

sinx.log(sinx)dx=log2-1
Limit of integration:0 to pi/2

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
5 years ago
Dear student

Please ask a question
Phanindra
226 Points
5 years ago
Put sinx = t... (1)then limits also will change...
Lower limit = 0 and upper limit = 1 
Now.. differentiate (1) that is cosxdx=dt  so..
dx = dt/cosx = dt/\sqrt{}(1-t^2)… 
Because ...sin2x + cos2x = 1...cosx = \sqrt{}(1-t^2)…
Now the question chages and its limits are...0 and 1...
Hope you have understood the steps...
This is the procedure...
You will get the answer..
If you do not get the answer..then tell me.i will send the full solution..
 
 

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