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1. (a) Find the sum of all the integers between 1 and 1000 which are divisible by 7. (b) Hence, or otherwise, evaluate the sum of (7r+2) from r=1 to r=142

1a) 1000/7=142.8.... Therefore there are 142 multiples of 7 between 1 and 1000 Therefore the sum of series from 1 to 142 is 1/7th of the solution Calculation:7 0.5 142 143=71071 1b) The sum of (7r+2) from r=...
JF
Answered by Jack F. • Maths tutor
6400 Views

Integrate sin^4(x)

sin^2(x) = (1 - cos(2x))/2 and cos^2(x) = (1 + cos(2x))/2so sin^4(x) = 0.25(1 - 2cos(2x) + cos^2(2x)) = 0.25(1 - 2cos(2x) + 0.5 + 0.5cos(4x))integrate = 3x/8 - sin(2x)/4 + sin(4x)/32
AN
Answered by Artem N. • Maths tutor
4663 Views

How do I choose which term do I differentiate/integrate when I am integrating by parts

What you would do in this scenario is consider all the terms in the expression you are integrating. You then want to go through the acronym LATE to choose which term you should differentiate.L stands for Log...
FP
Answered by Federico P. • Maths tutor
4166 Views

Integrate cos^2A

Integrating sin^2A and cos^2A is a bit nasty so we can use double angle formula to make it a little simpler. cos2A = cos^2A - sin^2A = 2cos^2A - 1. We can rearrange to get cos^2A in nicer terms. cos^2A = 1/2...
RM
Answered by River M. • Maths tutor
5139 Views

A curve has parametric equations x= 2sin(t) , y= cos(2t) + 2sin(t) for -1/2 π≤t≤ 1/2π , show that dy/dx = - 2sin(t)+ 1

A parametric equation is where both x and y are expressed separately, in terms of a parameter (t). In order to differentiate them we must use the chain rule, which here would be dy/dx= dy/dt ÷ dx/dt. The dif...
KL
Answered by Katie L. • Maths tutor
15583 Views