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How do I integrate terms with sin^2(x) and cos^2(x) in them? For example integrate (1+sin(x))^2 with respect to x

As you will be aware, it is not easy to directly integrate terms involving sin^2(x) and cos^2(x), so we use a substitution to turn them into something which we can integrate. From the double angle formula fo...
MH
Answered by Michael H. • Maths tutor
19146 Views

How do I add two fractions? (plus example)

Adding (and subtracting) fractions is more difficult than multiplying them because we need to make sure that the denominators (bottom numbers) are equal in both fractions. To do this, we may need to change t...
JB
Answered by Jenny B. • Maths tutor
5634 Views

How do I expand (x+a)(x+b)? (plus example)

The key to understanding expanding brackets is to understand that we need to multipy EVERYTHING in the first bracket by EVERYTHING in the second bracket. We can think of the calculation (x+a)(x+b) as x(x+b) ...
JB
Answered by Jenny B. • Maths tutor
17057 Views

How do I integrate by parts?

The integration by parts formula takes the form: int(uv') = uv - int(vu') where v' = dv/dx and u' = du/dx A lot of the art of using the integration by parts is working out which part to differentiate and whi...
CB
Answered by Chris B. • Maths tutor
5737 Views

How do you differentiate by first principles?

Firstly, what are we trying to achieve by differentiating a function? Differentiation allows us to compute the rate of change of a function at any point along a well behaved function. Consider the curve y = ...
DB
Answered by Daniel B. • Maths tutor
7496 Views