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How do I intregrate ln(x)?

To integrate ln(x) we will have to use integration by parts. The equation for integration by parts is: ( then equation written on the whiteboard ). In the case of ln(x), let v=ln(x) and let du/dx=1.Then dv/d...
IP
Answered by Isabelle P. • Maths tutor
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A cuboid has a rectangular cross section where the length of the rectangle is equal to twice its width x cm. THe volume is 81 cm^3. a) show that the total length L cm of the cuboid is given by L=12x+162/x^2

Volume=81 cm 3 b=81/2x 2 L=4x+4(2x)+ 4(b) L=4(x)+4(2x)+4(81/2x 2 ) L=12x+ 162/x 2
BT
Answered by Bilaal T. • Maths tutor
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How would you integrate ln x

You would use the product rule. uv'=uv- u'vdx. In this case we would allocate u= ln x and v'=1 so u'=1/x and v=x so uv=xlnx whilst u'v=x/x=1 so we would have xln(x) -1dx. Next we would get xln(x)-x +c
CM
Answered by Callum M. • Maths tutor
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A curve has the equation y=sin(x)cos(x), find the gradient of this curve when x = pi. (4 marks)

Option 1 - Differentiate using product rule giving dy/dx = cos 2 (x) - sin 2 (x). (2 marks) Subbing in x as pi (1 mark) then gives (-1) 2 + (0) 2 . Therefore the gradient is 1 (1 mark) . Option 2 - Initially...
MD
Answered by Mark D. • Maths tutor
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how do you differentiate y=x^2 from first principles?

let us start by taking two points on the curve y=x 2 , the first with x-coordinate x, and the second x+Δx and drawing a straight line between them. We can form a right-angled triangle, with two sides paralle...
CV
Answered by Christian V. • Maths tutor
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