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Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)

First use the substitution to find du/dx which is 2x. From this we now know that dx= du/2x (just re-arranging.) Substituting that into the integral we now get (6x³+4x)/ (sqrt (u) x 2x) du. Canc...

Answered by Khalil S. • Maths tutor

10005 Views

Let f(x)=x^3 - 2x^2 + 5. For which value(s) of x does f(x)=5?

Although it can be tempting to dive straight into such a question, its always useful in mathematics to take a step back and assess the question before scribbling down panicked answers.

For inst...

Answered by Jed G. • Maths tutor

3711 Views

Integrate lnx

This question often throws maths students off fairly easily as they are generally not taught the integral of lnx, and do not usually realise that integration by parts can be used for anything, as you can ...

Answered by Owen M. • Maths tutor

3402 Views

Find the coordinates of the stationary point of the graph y = 3x^2 - 12x

Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is ...

Answered by Jack M. • Maths tutor

6520 Views

w and x are whole numbers. w >40, x<30. Work out the smallest possible value of w-x.

To get the smallest value of w-x we will need the smallest value of w and the largest value of x.Our smallest possible value of w=41.Our largest possible value of x=29.So the smallest value of w-x = 41-29...

Answered by Esme G. • Maths tutor

15138 Views