One for the maths geniuses - Double Integration - PART 2!!
Discussion
Ok so I know how much you all loved last nights evening entertainment of maths homework so I have kindly prepared another for you all!!
Using double integration, find the area for x > 0 that is enclosed by the y axis, the curve y = 3 - x^2, and the line y = 2x
I have an answer, but reading back through the question I'm not so sure now as I don't know how to do it so it's just the value of area x above the x axis.
Anyways, answers on a postcard again.
I get 10.667
Using double integration, find the area for x > 0 that is enclosed by the y axis, the curve y = 3 - x^2, and the line y = 2x
I have an answer, but reading back through the question I'm not so sure now as I don't know how to do it so it's just the value of area x above the x axis.
Anyways, answers on a postcard again.
I get 10.667
Yup, one and two thirds. And no, this is not double integration, but involves two integrations.
The line y = 2x crosses the quadratic y = 3 - x^2 at x = -3 and x = 1.
The integration of 3 - x^2 is 3x - x^3/3 + c
The area between the x-axis and the quadratic over x = 0 and x = 1 is 3 - 1/3 = 2 2/3.
The integration of 2x is x^2 + c
The area between the x-axis and the line over x = 0 and x = 1 is 1
Therefore, area between quadratic and line is 2 2/3 - 1 = 1 2/3
The line y = 2x crosses the quadratic y = 3 - x^2 at x = -3 and x = 1.
The integration of 3 - x^2 is 3x - x^3/3 + c
The area between the x-axis and the quadratic over x = 0 and x = 1 is 3 - 1/3 = 2 2/3.
The integration of 2x is x^2 + c
The area between the x-axis and the line over x = 0 and x = 1 is 1
Therefore, area between quadratic and line is 2 2/3 - 1 = 1 2/3
Edited by V8LM on Sunday 13th December 08:56
V8LM said:
Yup, one and two thirds. And no, this is not double integration, but involves two integrations.
The line y = 2x crosses the quadratic y = 3 - x^2 at x = -3 and x = 1.
The integration of 3 - x^2 is 3x - x^3/3 + c
The area between the x-axis and the quadratic over x = 0 and x = 1 is 3 - 1/3 = 2 2/3.
The integration of 2x is x^2 + c
The area between the x-axis and the line over x = 0 and x = 1 is 1
Therefore, area between quadratic and line is 2 2/3 - 1 = 1 2/3
Alternatively just integrate 3 - x^2 -2xThe line y = 2x crosses the quadratic y = 3 - x^2 at x = -3 and x = 1.
The integration of 3 - x^2 is 3x - x^3/3 + c
The area between the x-axis and the quadratic over x = 0 and x = 1 is 3 - 1/3 = 2 2/3.
The integration of 2x is x^2 + c
The area between the x-axis and the line over x = 0 and x = 1 is 1
Therefore, area between quadratic and line is 2 2/3 - 1 = 1 2/3
Edited by V8LM on Sunday 13th December 08:56
It bothers me that I don't understand this.
I know I must've done this at school I sat & passed both Higher and Sixth Year Studies Maths.
Only relatively recently I had to look up how to do Long Division as I was surprised to discover I did not know how to do it, despite learning it at primary.
How much stuff have I forgotten already simply because I don't use it?
I know I must've done this at school I sat & passed both Higher and Sixth Year Studies Maths.
Only relatively recently I had to look up how to do Long Division as I was surprised to discover I did not know how to do it, despite learning it at primary.
How much stuff have I forgotten already simply because I don't use it?
AndyAudi said:
It bothers me that I don't understand this.
I know I must've done this at school I sat & passed both Higher and Sixth Year Studies Maths.
Only relatively recently I had to look up how to do Long Division as I was surprised to discover I did not know how to do it, despite learning it at primary.
How much stuff have I forgotten already simply because I don't use it?
Tell me about it, I was so embarrassed at work on Thursday as I just couldn't work out the percentage difference between two numbers. I felt slightly better when I passed it to the guy who sits opposite me and he couldn't do it either but even so!!I know I must've done this at school I sat & passed both Higher and Sixth Year Studies Maths.
Only relatively recently I had to look up how to do Long Division as I was surprised to discover I did not know how to do it, despite learning it at primary.
How much stuff have I forgotten already simply because I don't use it?
AndyAudi said:
It bothers me that I don't understand this.
I know I must've done this at school I sat & passed both Higher and Sixth Year Studies Maths.
Only relatively recently I had to look up how to do Long Division as I was surprised to discover I did not know how to do it, despite learning it at primary.
How much stuff have I forgotten already simply because I don't use it?
If it make you feel any better its sencond year degree level.I know I must've done this at school I sat & passed both Higher and Sixth Year Studies Maths.
Only relatively recently I had to look up how to do Long Division as I was surprised to discover I did not know how to do it, despite learning it at primary.
How much stuff have I forgotten already simply because I don't use it?
Sorry, but what degree? K87 said:
Automotive engineering. The annoying thing is I know I will never use it, thats what computer programmes are for these days!
Do the programmes write themselves? Noo, thats why you need to understand it.Wait till year three and you'll have to do manual checks to confirm FEA & CFD analyses.
K87 said:
Automotive engineering. The annoying thing is I know I will never use it, thats what computer programmes are for these days!
I used to say that (when I was doing integration at 'O' level - old git me) but now make a living writing computer software. I also find it curious why calculus was dropped from both GSCE and, more worringly, 'A' levels. What replaced it?V8LM said:
K87 said:
Automotive engineering. The annoying thing is I know I will never use it, thats what computer programmes are for these days!
I used to say that (when I was doing integration at 'O' level - old git me) but now make a living writing computer software. I also find it curious why calculus was dropped from both GSCE and, more worringly, 'A' levels. What replaced it?V8LM said:
K87 said:
Automotive engineering. The annoying thing is I know I will never use it, thats what computer programmes are for these days!
I used to say that (when I was doing integration at 'O' level - old git me) but now make a living writing computer software. I also find it curious why calculus was dropped from both GSCE and, more worringly, 'A' levels. What replaced it?I certainly covered calculus in my A-Level exam in '91 and was tutoring a boy a few years ago and he was learning it too. Have they really taken it off the A-Level syllabus? I can't believe universities would be accepting Maths undergraduates without having already covered calculus.
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