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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 (xln(x) - int(x(1/x))) = x*ln(x) - x

Therefore, evaluating between 2 and 4 gives us (4ln(4) - 4) - (2

KR
Answered by Kyle R. Maths tutor
4091 Views

if x^2 + 9x + 20 = 0, what are the possible values of x?

So x2 + 9x + 20 = 0 My preffered way of solving this equation is to factorise the equation. (Though I understand that different students may find other ways easier) Factorisation is where the a...

TP
Answered by Tilly P. Maths tutor
10820 Views

How do I find the equation of a straight line?

Let's draw a line. It crosses the point (0,1), intercepting the y-axis (remember, y to the sky!) at 1 and the x-axis at the point (-2,0).

An equation tells us what a line looks like, it's...

DG
Answered by Dominique G. Maths tutor
6663 Views

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)t...

OD
Answered by Owain D. Maths tutor
13324 Views

x = 0.045 (45 recurring). Prove algebraically that x can be written as 1/22

x=0.045 (45 recurring)

10x = 0.45 (45 recurring)

100x = 4.54 (54 recurring)

1000x = 45.45 (45 recurring)

To get rid of the decimals:

<...

JT
Answered by John T. Maths tutor
60066 Views

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