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How can I remember the difference between differentiation and integration?

A neat trick to remember what we do to the powers when integrating and differentiating is that we IN crease the power when we IN tegrate, and D ecrease the power when we D ifferentiate! Once we've got the po...
LW
Answered by Laura W. • Maths tutor
19747 Views

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 add ...
LW
Answered by Laura W. • Maths tutor
4837 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 parts works when you have...
IE
Answered by Isaac E. • Maths tutor
6112 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. By doing ...
MP
Answered by Minh P. • Maths tutor
16067 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/dx)dx T...
SA
Answered by Sammy A. • Maths tutor
6605 Views