How to solve this integral without using substitution method? As I'm curious that is there another method to solve integral? I did integration by parts.
∫√4−x2dx=x√4−x2+∫x2√4−x2dx
=x√4−x2−∫4−x2√4−x2dx+∫4√4−x2dx
=x√4−x2−∫√4−x2dx+4sin−1(x2)
2∫√4−x2dx=x√4−x2+4sin−1(x2)
∫√4−x2dx=12x√4−x2+2sin−1(x2)
Is there any other method can solve integral other than substitution and this? I think Riemann Sum also can be used to solved. But people riemann sum is not considered a method of integration. I wonder why. Thanks a lot.
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