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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 = ...
KR
Answered by Kyle R. • Maths tutor
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Given that d/dx(cosx)=-sinx show that d/dx(secx)=secx(tanx)

let y=sec(x) = 1/(cos(X)) = cos(x) -1 Thus dy/dx = -1(cos(x)) -2 (-sinx) = sin(x)/(cos(x)) 2 = 1/cos(x) x sin(x)/cos(x) =sec(x)tan(x)
OD
Answered by Owain D. • Maths tutor
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Understanding HIV, vaccines and monoclonal antibodies

To understand how HIV causes infection, students should have an appreciation for its basic virus structure and how it infects humans. Following infection, how does it cause disease and eventually AIDS? Why a...
SS
Answered by Subi S. • Biology tutor
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“The Fool knows that the only true madness is to recognise this world as rational.” How far is this an adequate explanation of King Lear?

The role of the Fool in William Shakespeare’s 1606 play ‘King Lear’ is fundamental to the strong narrative voice of the play, showcasing both themes of madness and rationality. As Isaac Asimov said in his ‘G...
CR
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Explain how pH changes can be minimised using a mixture of a weak acid and it's conjugate base

This mixture of a weak acid (HA) and it's conjugate base (A - ) acts as a buffer . A buffer is a solution with a highly stable pH. On addition of small amounts of either a strong acid or a strong base, this ...
CT
Answered by Cora T. • Chemistry tutor
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