Alan

Here's one way of doing integral 2xsin^3x dx step by step:

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a). f(g(x)) = 1/(x^2 + 5x)

b) This graph should help you to answer this:

Yes.

Think about taking a small step, deltax, away from zero. If y(0) = 1 then dy/dx is non zero at x=0 and will start to change the value of y.  However, if y(0) = 0, then day/dx is zero and hence is unable to give rise to a change in y, so at deltax the value of y is still zero. Repeating this for another step of deltax therefore still doesn't lead to a change in y.  y stays at zero for all x.

Here is a numerical solution comparison using initial conditions 0 (yy) and 1 (y)

You can see that although y(0) = 1 gives rise to a changing curve, y(0) doesn't.

Then the solution is y(x) = 0 for all x.

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Use the fact that mass = density * volume

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If y(0) = 0 then dy/dx(0) = 0 as well. This means y never changes from zero!

Are you sure y(0) = 0?

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Standard error on the mean is standard deviation/sqrt(sample size) = 5/7 ≈ 0.714

Number of standard errors between 50 and 47.7 = (50 - 47.7)/0.714 ≈ 3.22

Probability of being more than 3.22 standard errors away from the mean on a normal distribution ≈ 0.0007

Hence probability sample average is greater than 47.7 is ≈ 0.9993

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