The Student Room Group

Integration

Screenshot_20160521-123408.jpg

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 ?
Original post by Ravster
Screenshot_20160521-123408.jpg

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 ?


you answered your own question

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
(edited 7 years ago)
Reply 2
Original post by thefatone
you answered your own question

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.
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
Reply 4
Original post by thefatone
you answered your own question

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?
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
Reply 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?


Nopes... the area that you find via integration is the blue area below.

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