Question

Use inscribed rectangles to approximate the area under g(x) = –0.5x2 + 7 for –3 ≤ x ≤ 0 and rectangle width 0.5.

Answer 1

this is a Reimann sums problem
\[g(x)=-0.5x^2+7\\
h=0.5\\
a=-3\qquad b=0\\
N={b-a\over h}={3\over 0.5}=6\\
\text{Let us use left-hand sums}\\
x_0=a=-3\qquad\qquad g(x_0)=-0.5(-3)^2+7=2.5\\
x_1=a+h=-2.5\quad g(x_1)=3.875\\
x_2=a+2h=-2\quad g(x_2)=5\\
\vdots\\
x_5=a+5h=-0.5\quad g(x_5)=6.875\\
\;\\
\text{approximation of the area is:}\\
A\approx h\sum_{k=0}^{N-1}g(x_k)\\
A\approx h\left[2.5+3.875+5+\ldots+6.875\right]=?
\]

Answer 2

you follow?

Answer 3

um, no, im confused on the last part