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What are the advantages of using numerical integration (Trapezium rule, Simpson's rule and so on) over direct integration?

Numerical methods are particularly useful to solve complex problems which are sometimes difficult or impossible to solve analytically. It is also a quicker way of solving the problem rather than using formul...
PA
Answered by Priyanka A. • Maths tutor
16208 Views

A triangle has sides A, B and C. The side BC has length 20cm, the angle ABC is 50 deg and angle BAC is 68 deg. a) Show that the length of AC is 16.5cm, correct to three significant figures. b) The midpoint of BC is M, hence find the length of AM

a) The answer to this question is quite simple, it is all dependent on the pupil realising that they need to use the sine rule. This rule for this triangle is: BC/sin(BAC) = AC/sin(ABC) Once they get this eq...
RS
Answered by Ravi S. • Maths tutor
5867 Views

How do I find the inverse of a 2x2 matrix?

Hiya! So the very first thing we need to do is find the determinant, which is just a fancy word to describe a matrix; for a 2x2 matrix, it's equal to "ad-bc", where: (a b c d) This will give you a ...
NC
Answered by Namir C. • Maths tutor
6165 Views

What is the value of the integral of e^x from x = 1 to x = 2?

As the derivative of e^x is e^x, so is the integral (plus some constant). As we wish to find the value of the integral from x = 1 to x = 2, we substitute x=2 into e^x, and from that we subtract e^x with x=1....
JH
Answered by Jake H. • Maths tutor
4672 Views

Express x^2 + 5x + 10 in the form (x+p)^2 +q

x^2+5x+10 -> (x+p)^2+q (x+5/2)^2 - (5/2)^2 + 10 (x+5/2)^2 - (25/4) +40/4 (x+5/2)^2 +15/4
IB
Answered by Imogene B. • Maths tutor
6505 Views