#Integration A1

72 messages · Page 1 of 1 (latest)

crimson panther
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Can some1 explain what theyd do for part C?

image.png
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btw i checked mark scheme for the other answers and their right so dw about the working out

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dense idol
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So if you integrate the curve from 0 to 5 you'll get the area above the curve

crimson panther
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yeah to the x axis

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i get that

dense idol
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Ok so draw a line from 5,–13 to the x axis

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Now you got a trapezium

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Get the area of that trapezium and subtract the area above the curve

crimson panther
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ah alright

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is there any alternative methods u could use

dense idol
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No

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Not that ik of

crimson panther
crimson panther
dense idol
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Oh

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So you know when you want to get the intersection between 2 curves or a line and a curve

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You equate the together

crimson panther
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yh

dense idol
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Then collect them on one side and let the other equal 0

crimson panther
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yhyh

dense idol
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When you do that you let the points of intersection between the curve and the line be points of intersection with the x axis

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Its like you got an equation of a curve equal to 0

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And you are getting its roots

crimson panther
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ok

dense idol
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You get it?

crimson panther
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no

crimson panther
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idk what u mean

dense idol
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Ok I'll give you an example

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One sec

crimson panther
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kk

dense idol
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You got a curve with equation x^2 +3x–9

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And a line x–3

crimson panther
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okay

dense idol
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Now they meet at two points

crimson panther
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yeah

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x^2 + 2x -6?

dense idol
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–3,–6 and –1,–1.4

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These are the points of intersection

crimson panther
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ok

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yeah

dense idol
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Equal to 0

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So that means that this x^2+2x–6 intersects with the x axis at the same x coordinates as the points of intersection

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Cause when you got x^2+2x–6 you're essentially getting the roots of that curve

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Which is also the coordinates of the points of intersection of the original curve and line

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You lost?

crimson panther
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oh

crimson panther
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i understand everything u say after

dense idol
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Ok so when you solve that equation

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Its solutions are the x coordinates of the intersections right

crimson panther
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yep

dense idol
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and in another context when you solve that equation you are getting the roots of the curve x^2+2x–6

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And roots mean the intersection of the curve with the x axis

dense idol
crimson panther
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ohhhhhhhh

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i get u now

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shitttt

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yh

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so basically

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ur working out

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the formula for the points of intersection by combining them

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and u know youll use the points 5 and 0

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so just integrate the combined formula using them points

dense idol
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Yea so basically what the ms did is they pulled the curve upwards so that the intersections are on the x axis so when you integrate you'll get that shaded area alone cause it'll be above the x axis on its own

dense idol
dense idol
crimson panther
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yh i get u now

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thanks for helping me