Search over 10,000 free study notes

We can use the formula for a Volume of Revolution: V =π ∫ (e^x + e^(-x))^2 dx, with limits x = 0, x = ln4.Expanding the brackets: (e^x + e^(-x))^2 = e^2x + 2 + e^(-2x).So: V = π ∫ (e^2x + 2 + e^(-2x)) dx ...

The main thing to consider here is the output of the operation. Vector and scalar products are both operations in which you take two vectors but then get something else. In a scalar product, you get a num...

Step 1) x²+2x+4 = (x+1)²+3Step 2) Minimum point occurs at (-1, 3)
I can use the whiteboard to explain it better.

(I can use the whiteboard for to explain it better)1) Express y = ln(x) as y = ln(x) * 12) Use integration by parts with u = ln(x), v'=(1), u'=1/x, v = xintegral = xln(x) - integral(x*1/x) =xln(x) - integ...

One way education levels vary in and between countries is through designated levels of government spending. For instance, levels of government spending on education in France and the UK, two highly-develo...