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Integrate 1/(5-2x) for 3≤x≤4

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one to...
ES
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Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

First we state the formula for sin(x+y) sin(x+y) = sin(x)cos(y) + cos(x)sin(y) Letting y = 2x sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x) Now sin(2x) = 2sin(x)cos(x) and cos(2x) = 1 - 2sin^2(x), substitute the...
KR
Answered by Kyle R. • Maths tutor
22980 Views

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
4323 Views

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

So x 2 + 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 above equation...
TP
Answered by Tilly P. • Maths tutor
11839 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 a way of describing...
DG
Answered by Dominique G. • Maths tutor
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