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How do you integrate?

Ok so there are two basic steps to integrating a function: You add 1 to the power of any x term. e.g. x 2 -> x 3 , 2x 7 -> 2x 8 , 3 = 3x 0 -> 3x You divide the term by the new power e.g. if the new ...
JS
Answered by Jeremy S. • Maths tutor
4353 Views

Find the indefinite integral of cos^2 x

First, we need to write cos 2 x in a form that is easily integrable. We can use the double angle formula cos(2x) = 2cos 2 x - 1 to see that cos 2 x = 1/2cos(2x)+1/2. Now, we can integrate the terms seperatel...
ER
Answered by Ethan R. • Maths tutor
10711 Views

How do I solve simultaneous equations by substitution?

Often, substitution is used when dealing with quadratic simultaneous equations as the other method, elimination, is more straightforward and can be used to solve linear equations but it cannot be used for qu...
NM
Answered by Niamh M. • Maths tutor
6362 Views

Hannah's sweet problem (Edexcel 2015): There are n sweets, 6 are orange, rest of the sweets are yellow. She takes 2 sweets randomly without replacing them and the probability that 2 orange sweets are chosen is 1/3. Show that n^2-n-90 = 0.

Draw a probability tree diagram. For this question, only two branches are required (orange and orange). At the start, there are n sweets in total, 6 are orange, so p(O) = 6/n. On our second pick, there are 5...
YZ
Answered by Yimin Z. • Maths tutor
5688 Views

Karen got 32 out of 80 in a maths test. She got 38% in an English test. Karen wants to know if she got a higher percentage in maths or in English. Did Karen get a higher percentage in maths or in English?

We are given that Karen got 38% in her English test, so all that's left to do is work out the percentage she achieved in her maths test and then compare it with 38%: We calculate the percentage by taking 32/...
HC
Answered by Hal C. • Maths tutor
8357 Views