Eric Nicholas K's answer to Rachel's Junior College 2 H2 Maths Singapore question.
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I have used the double angle formula for sin and cos several times in the integration and simplification.
Date Posted:
4 years ago
Checking with software suggests that the -1/16 cos-¹(2u) should be 1/16 sin-¹(2u) instead, but your working looks ok to me. Not sure what went amiss
Later I check once again. Could be the angle range or some misintegration.
Doesn't seem to be. I think I know already, it's got to do with the constant.
The two expressions give the same result when differentiated. Should be ok since d/dx sin-¹(x) = 1/√(1-x²) = -d/dx cos-¹(x)
The two expressions give the same result when differentiated. Should be ok since d/dx sin-¹(x) = 1/√(1-x²) = -d/dx cos-¹(x)
Later I try and inspect the equation using the similar looking 2u = sin x
Apparently using 2u = sin x did make the result 1/16 times sin-1 (2u) + the rest.
Yea I tried it too. Works
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