AS maths Integration Watch

Mell x
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Hey, I'm currently stuck on a maths problem for integration ( finding the area under a curve ) I was wondering whether anyone could help me with it?

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Everything else is fine but I am really struggling on how to work out the area of the shaded regions, especially since there is another line on the graph.

Could someone explain how I would work out 5c) and 8a) please ?
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Kvothe the Arcane
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(Original post by Mell x)
Hey, I'm currently stuck on a maths problem for integration ( finding the area under a curve ) I was wondering whether anyone could help me with it?

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Size:  3.8 KBName:  maths2.jpg
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Everything else is fine but I am really struggling on how to work out the area of the shaded regions, especially since there is another line on the graph.

Could someone explain how I would work out 5c) and 8a) please ?
Have you ever been taught the formula
\displaystyle A_{\text{between \ two \ curves}}=\int_a^b f(x)-g(x)dx?
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Mell x
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(Original post by keromedic)
Have you ever been taught the formula
\displaystyle A_{\text{between \ two \ curves}}=\int_a^b f(x)-g(x)dx?
No, I don't think so
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Kvothe the Arcane
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(Original post by Mell x)
No, I don't think so
Have you ever done problems in regular geometry where you had to find the area of a shaded region by subtracting an area from another?


Like finding the area of the yellow regions in the above diagram.
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Mell x
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(Original post by keromedic)
Have you ever done problems in regular geometry where you had to find the area of a shaded region by subtracting an area from another?


Like finding the area of the yellow regions in the above diagram.

Yes I did. I worked out 5c) to be 8 by subtracting the area under the curve from the area of the triangle.

However, I'm still not sure on 8a)
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Kvothe the Arcane
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(Original post by Mell x)
Yes I did. I worked out 5c) to be 8 by subtracting the area under the curve from the area of the triangle.

However, I'm still not sure on 8a)
It's really hard to see. Is it possible you to upload a clearer pic?
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Mell x
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(Original post by keromedic)
It's really hard to see. Is it possible you to upload a clearer pic?
Yeah sure
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Kvothe the Arcane
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(Original post by Mell x)
Yeah sure
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You can use the same method. What's the problem?
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Mell x
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(Original post by keromedic)
You can use the same method. What's the problem?
I've integrated it and used the values 1 and 4 for the area but this gives 14.25, whereas the book says that it's supposed to be 6.75
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(Original post by Mell x)
I've integrated it and used the values 1 and 4 for the area but this gives 14.25, whereas the book says that it's supposed to be 6.75
14.25 is the difference between the two areas?
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Mell x
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(Original post by keromedic)
14.25 is the difference between the two areas?
Yeah I think so
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Kvothe the Arcane
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(Original post by Mell x)
Yeah I think so
Please paste your working using Latex and I'll point out any errors
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Mell x
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(Original post by keromedic)
Please paste your working using Latex and I'll point out any errors
I'm not sure on how to find/ or use that software Is it alright if I just tyoe and use '^' for the powers symbol? e.g x^2, xsquared

I integrated the curve line to be 1/4x^4 - 2x^3 + 7/2x^2 + 8x

when x=4, 1/4(4)^4 - 2(4)^3 + 7/2(4)^2 + 32 which equals 24

when x=1, 1/4 - 2 + 7/2 +8 which equals 39/4

the area was 24-39/4 which is 57/4
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(Original post by Mell x)
I'm not sure on how to find/ or use that software Is it alright if I just tyoe and use '^' for the powers symbol? e.g x^2, xsquared

I integrated the curve line to be 1/4x^4 - 2x^3 + 7/2x^2 + 8x

when x=4, 1/4(4)^4 - 2(4)^3 + 7/2(4)^2 + 32 which equals 24

when x=1, 1/4 - 2 + 7/2 +8 which equals 39/4

the area was 24-39/4 which is 57/4
You've not taken that away from the area between the line and the x axis. I.e. a trapezium
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Mell x
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(Original post by keromedic)
You've not taken that away from the area between the line and the x axis. I.e. a trapezium
I don't understand, what do you mean? :confused:
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(Original post by Mell x)
I don't understand, what do you mean? :confused:
You've found the area between the curvy graph and the x axis. But what you really want is the area between the straight line and the curve, the shaded region.
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Mell x
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(Original post by keromedic)
You've found the area between the curvy graph and the x axis. But what you really want is the area between the straight line and the curve, the shaded region.
oh, which values would I need to substitute for that?
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