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Maths
A Level

integrate ln(x) using integration by parts

xlnx - x 

KB
Answered by Kofi B. Maths tutor
3730 Views

Simplify √32 + √18 giving your answer in the form of a√2.

√32 + √18

= 4√2 + 3√2

= 7√2

KS
Answered by Kavi S. Maths tutor
8579 Views

A stone, of mass m , falls vertically downwards under gravity through still water. The initial speed of the stone is u . Find an expression for v at time t .

  1. Ma = mg - Lmv        2) dv/dt = g-Lv 3)-1/L *(ln(g -Lv)/(g - Lu)) = t             4) g - Lv/ g - Lu = e-Lt 5) Rearrange to.... v = 1/L *(g-(g - Lu) e-Lt) Missed some steps as i...
JW
Answered by Joseph W. Maths tutor
3869 Views

What is the cosine rule and how do I use it?

The cosine rule,

a2=b2+c2-2bccosA,

where a, b, & c are the sides of a triangle and A is the angle opposite side a, is the general version of Pythagoras' ...

MQ
Answered by Matt Q. Maths tutor
5819 Views

Find the derivative of f(x)= ln(|sin(x)|). Given that f(x) has a value for all x, state why the modulus is required.

The derivative can be found by using the chain rule. i.e. let g(x) = |sin(x)|, so f(x)=ln(g(x)), hence df/dx = df/dg * dg/dx

df/dg = 1/g, dg/dx = |cos(x)| so df/dx = |cos(x)|/|sin(x)|

For th...

LK
Answered by Luke K. Maths tutor
10649 Views

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