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(In tandem with the whiteboard) Integration is a way of working out the total of something. An example of this is if you see a graph of velocity and time, the area under the graph is the total distance tr...

Making a substitution for u = 2x^2 Now y = ln(u) dy/dx = du/dx * dy/du du/dx = 4x dy/du = 1/u dy/dx = 4x/u Then substitute 2x^2 back in as u The final answer is 4x/(2x^2) Which can be simplified by divid...

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Since Rsin(x+y)=Rsin(x)cos(y)+Rsin(y)cos(x), we can set Rcos(y)=4 (1) and Rsin(y)=3 (2) on comparison to the desired equation. Considering (2) divided by (1) we see that tan(y)=sin(y)/cos(y)=3/4 so y=atan...

The answer to this question depends on one thing, whether this power is odd or even.

For even powers we use the identity cos(2x) = 2cos^2(x)-1 = 1-2sin^2(x). So for example, the integral of cos^2(x...