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

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

Answer 1

Which ones are you having trouble with?

Explanation:

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)`