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Maths
A Level

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...

ES
6791 Views

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(2...

KR
Answered by Kyle R. • Maths tutor
21711 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 (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
3756 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
12668 Views

How do I use the chain rule for differentiation?

The chain rule is used when we have a function in the form f(g(x)).

For example sin(x^3). [In this case, f(x) = sin(x) and g(x) = x^3]

The chain rule says that the derivativ...

TK
Answered by Tom K. • Maths tutor
4940 Views

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