  In solving the integration of: (sin x) / (1+ cos x)  [0, pi/2] where u= (1+ cos x) and du = -sin x dx, the solution converted the interval of [0, pi/2] to [2, 1].       I don't understand why this was necessary since the order of the intervals seem reversed. Could you give me a step by step explanation why this was necessary?

Question

In solving the integration of: (sin x) / (1+ cos x)  [0, pi/2] where u= (1+ cos x) and du = -sin x dx, the solution converted the interval of [0, pi/2] to [2, 1].       I don't understand why this was necessary since the order of the intervals seem reversed. Could you give me a step by step explanation why this was necessary?

Step 1

The function is

Step 2

To compute: help_outlineImage Transcriptioncloseя sin x d 0 1+cosX Take 1 cosx= t; differentiate it with respect to t. d (1cosx) dt dt dt dx 1 -sin x dt -sin xdx dt sin xdx dt At x 0, the value of t becomes t =1+ cos(0)=1+1= 2 п the value oft becomes t = 1 +cos] 2 At x - =1+0 1 - fullscreen
Step 3

Thus, the definite integral with...

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Calculus 