Find, approximate, the area under f(x)=3x^2+6x +3 [-3,1] using the given partitions? a) 4 upper sum rectangles b) 2 midpoint rectangles c) 2 trapezoids d) 256 right sided rectangles

Question

Find, approximate, the area under f(x)=3x^2+6x +3 [-3,1] using the given partitions:
a) 4 upper sum rectangles
b) 2 midpoint rectangles
c) 2 trapezoids
d) 256 right sided rectangles

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Answer 1 · 2016-11-18T23:38:57

Which ones are you having trouble with?

graph{3x^2+6x+3 [-14.44, 14.03, -0.74, 13.5]}

(a) #12(1)+3(1)+3(1)+12(1) = 30#

(b) #3(2)+3(2) = 12#

(c) #1/2(12+0)(2) + 1/2(0+12)(2) = 12+12=24#

(d) #sum_(i=1)^256 (3(-3+i/64)^2+6(-3+i/64) + 3) = (32,769)/(2,048)#