Search our library of Maths questions

Top answers

Maths

All levels

Use integration by parts to integrate ∫ xlnx dx

∫ u(dv/dx) dx = uv − ∫ v(du /dx)dx is the Integration by Parts formula.

If you set u=lnx, differentiation (rememeber from tables) leads to du/dx= 1/x, and dv/dx=x and so v=x^2/2 (raise power by on...

Answered by Minty M. • Maths tutor

20879 Views

A circle with centre C(2, 3) passes through the point A(-4,-5). (a) Find the equation of the circle in the form (x-a)^2 + (y-b)^2=k

This question is aimed at A-Level Pure Core 1 students. A circle with centre C(2, 3) passes through the point A(-4,-5). Find the equation of the circle in the form (x-a)^2 + (y-b)^2 = k ...

Answered by Tilly C. • Maths tutor

5041 Views

i) Make y the subject of the expression x = ((a-y)/b))^1/2 ii) Simplify fully (2x^2 − 8)/(4x^2 − 8x)

i) Square both sides of the expression to make x^2=(a-y)/b

Multiply by b to remove the fraction from the equation and then rearrange to make y the subject.

bx^2=a-y --> y=a-bx^2

i...

Answered by Oscar S. • Maths tutor

4448 Views

Differentiate x^3 − 3x^2 − 9x. Hence find the x-coordinates of the stationary points on the curve y = x^3 − 3x^2 − 9x

To differentiate, we bring the power down and decrease the power by 1. So x³ becomes 3x², -3x² becomes -6x, and -9x (which can be written as -9x¹ ) becomes -9. ...

Answered by Tutor105800 D. • Maths tutor

10395 Views