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What are Prime Numbers?
Prime numbers by definition are numbers that cannot be divided by any other number but itself and 1. For e.g. 2 is a prime as it can only be divided by 2 and ...

The key is to look at the first and second derivatives of that function. Remember that a turning point always has the first derivative equal to zero. Then, the sign of the second derivative indicates if t...

Starting with x=2cosu, rearrange for u to get u=arccos(x/2), then find the upper and lower limits of the integral. We find that our lower limit goes from 1 to pi/3, ad our upper limit goes from root 2 to ...

1/2 *e^(x)(sin x -cos x)

Use integration by parts to obtain:u=arcsin(x), u'=1/(1-x²)^0.5, and v'=1, v=x
Using the equation: integral of uv' = uv - integral of u'vintegral of arcsin(x) = xarcsin(x) - inte...