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How do I do integration by substitution?

There are a number of integrals that we can evaluate directly, called elementary functions:integral[ x dx ] = x 2 /2 + Cintegral[cos( x ) dx ] = sin( x ) + C However, most integrals cannot be solved so direc...
MT
Answered by Matthew T. • Maths tutor
6665 Views

What are the possible value(s) of x for the following: x^2 + 3x - 54 = 0

It is a quadratic equation and when factorised will be of the form (x +/- a) (x +/- b) = 0. We need to find 2 numbers, a and b, that add together to make the 3 for the 3x term and which are multiplied togeth...
KG
Answered by Kate G. • Maths tutor
5874 Views

Bob lives 2km away from Alice and the school is 1km away from Bob. Alice sets off to meet Bob at 8am and she meets him at 8:15 and they carry on walking at the same pace. School starts at 8:20. Do they get to school on time? How early/late are they?

Many pupils struggle when maths questions that are given in a very wordy format. I feel these types of questions can be the most useful in testing mathematical concepts that the pupils have picked up in less...
MK
Answered by Marcin K. • Maths tutor
4568 Views

Differentiate the function y=(6x-1)^7

Problems of this style are solved using the chain rule. To begin, define the quantity inside the brackets as u u = 6x-1 such that y = u^7 It is now useful to write the chain rule. We can see dy/dx = du/dx x ...
JL
Answered by Jamie L. • Maths tutor
5213 Views

Which A-level modules did you take?

C1, C2, C3, C4 M1, M2, M3 S1, S2, S3 FP1, FP2
MW
Answered by Michael W. • Maths tutor
5271 Views