Search our library of Maths questions

Top answers

Maths

All levels

How should I go about factorising x^2+5x+6?

I always think of the middle number as the sum and the last number as the product (in this example, we have the sum as 5 and the product as 6!) This just means that we have to look for two numbers which a...

Answered by Laura W. • Maths tutor

4322 Views

How do you integrate by parts?

This is one of the trickiest methods of calculus on the course, but it's important to know, and is very doable if you set up the problem right and remember the steps.

Integration by part...

Answered by Isaac E. • Maths tutor

5622 Views

The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). Show that P lies on C.

Every point on the curve C satisfies the equation. In order to show P lies on C, we need to test if either x- or y-coordinates satisfy the equation. It is easier to subsitute x=2 into the equation.

...

Answered by Minh P. • Maths tutor

15250 Views

Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C

Starting with the initial integral of int(exp(x).cos(x))dx we can see that this is going to have to be integrated by parts. This states that the integral of (u . dv/dx)dx is equal to u.v - int(v . du/d...

Answered by Sammy A. • Maths tutor

5986 Views

A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

To find the gradient of any curve, we take the derivative. So in this case, we need to take dy/dx. We do this by multiplying the term by the power on x, and then lowering the power by one. For example, fo...

Answered by Elizabeth H. • Maths tutor

5706 Views