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# Integration watch

1. Part C:

the coordinates of N are (0,-168)

to find the area I integrated between x=0 and 4 and that's as far as I got.

In the mark scheme they have found the area of the rectangle and subtracted the area between 0 and 4.

Can someone explain what I'm missing here ?
2. (Original post by Ravster)

Part C:

the coordinates of N are (0,-168)

to find the area I integrated between x=0 and 4 and that's as far as I got.

In the mark scheme they have found the area of the rectangle and subtracted the area between 0 and 4.

Can someone explain what I'm missing here ?

but you need to find the area of the rectangle from O to N to P to 4

integrate to find area under the curve between 0 and 4 like you said then minus area of rectangle by area under the curve
3. (Original post by thefatone)

but you need to find the area of the triangle from O to N to P to 4

integrate to find area under the curve between 0 and 4 like you said then minus area of triangle by area under the curve
A triangle has straight lines. This isn't a straight line. Hence it's not a triangle.
4. (Original post by Zacken)
A triangle has straight lines. This isn't a straight line. Hence it's not a triangle.
good point i'll change it to rectangle
5. (Original post by thefatone)

but you need to find the area of the rectangle from O to N to P to 4

integrate to find area under the curve between 0 and 4 like you said then minus area of rectangle by area under the curve
That's what I don't understand.

By integrating between 0 and 4 aren't we then left with the area of the shaded region?

Why do we need to involve the rectangle?
6. (Original post by Ravster)
That's what I don't understand.

By integrating between 0 and 4 aren't we then left with the area of the shaded region?

Why do we need to involve the rectangle?
No that's the bit you missed, By integrating between 0 and 4 you get the area between the curve and x-axis

involving the rectangle which includes all of the shaded area and the area between the curve and x-axis is what you need
7. (Original post by Ravster)
That's what I don't understand.

By integrating between 0 and 4 aren't we then left with the area of the shaded region?

Why do we need to involve the rectangle?
Nopes... the area that you find via integration is the blue area below.

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