Hi, I am doing a worksheet for tomorrow's Calc class and I can't solve the following question! Can someone please explain to me how this is done?
Find the upper and lower sums of f(x)=-2x+4
Interval: [0, 2]
4 subintervals equal in length
I am just so lost with this one and my book doesn't have any examples on how to work this specific problem. Any help would be great. THANKS!!!! :)
Find the upper and lower sums of f(x)=-2x+4
Interval: [0, 2]
4 subintervals equal in length
I am just so lost with this one and my book doesn't have any examples on how to work this specific problem. Any help would be great. THANKS!!!! :)
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4 intervals, so interval width is 2/4 = 1/2.
summing with left edge determining height,
S = ½(f(0) + f(1/2) + f(1) + f(3/2))
S = ½(4 + 3 + 2 + 1)
S = 5
summing with right edge determining height,
S = ½( f(1/2) + f(1) + f(3/2) + f(2))
S = ½(3 + 2 + 1 + 0)
S = 3
average of the 2 values is 4
and area of the triangle is ½•base•height = ½(2)(4) = 4
summing with left edge determining height,
S = ½(f(0) + f(1/2) + f(1) + f(3/2))
S = ½(4 + 3 + 2 + 1)
S = 5
summing with right edge determining height,
S = ½( f(1/2) + f(1) + f(3/2) + f(2))
S = ½(3 + 2 + 1 + 0)
S = 3
average of the 2 values is 4
and area of the triangle is ½•base•height = ½(2)(4) = 4