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Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Using integration by parts, we can re-write the integral of ln(x) as (x ln(x) - int(x (1/x))) = x*ln(x) - x Therefore, evaluating between 2 and 4 gives us (4 ln(4) - 4) - (2 ln(2) - 2) = 2ln(16/2) - 4 + 2 = ...
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Answered by Kyle R. • Maths tutor
4216 Views

Why is centripetal acceleration directed inwards to the centre of the circle during centripetal motion? If I’m in a car while it’s cornering, I seem to be pushed outwards away from the centre, not inwards.

When I initially met this problem, I was slightly confused because of the car analogy above. So the way to think about this is that your body and the car are separate, and just as the car starts going around...
RG
Answered by Rudolfs G. • Physics tutor
5498 Views

Why are UK government gilt (bond) yields rising and why is that bad?

A bond or a gilt is a way of borrowing money for corporations or governments. For example, if an imaginary government wanted to borrow $100, it could issue a single bond, and an investor could buy that bond ...
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Answered by Rudolfs G. • Economics tutor
26979 Views

Explain the formation of a waterfall

As water flows over underlying rocks, it erodes softer rock much faster than harder rock. This creates a small step in the stream or river. Explaining the formation of waterfalls As water flows over underlyi...
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Answered by Ellen L. • Geography tutor
46991 Views

Am I expected to remember certain figures/dates for my exam?

If you don't know it, don't include it. The examiner will not be impressed with your ability to memorise a date down to the exact day/month/year, but will instead award marks for you ability in showing how t...
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Answered by Oscar R. • History tutor
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