Question

Reimann sum and area of integral help

Answer 1

can someone please do no 13?

Answer 2

base is 2, using 30 rectangles each has base of
\[\frac{30}{2}=\frac{1}{15}\]

Answer 3

that is your \[\Delta x\]

Answer 4

circumscribed means in this case right hand endpoints so
\[x_1=1+\frac{1}{15}\]
\[x_2=1+\frac{2}{15}\]
and in general

\[x_k=1+\frac{k}{15}\]

Answer 5

your function is
\[f(x)=3x^2\] so
\[f(x_k)=3(1+\frac{k}{15})^2\]

Answer 6

multiply this by
\[\Delta x=\frac{1}{15}\] and add

Answer 7

you get \[\sum_{k=1}^n 3(1+\frac{k}{15})^2\frac{1}{15}\]

Answer 8

you can do the inscribed ones exactly the name mutatis mutandis

Answer 9

whoops

Answer 10

was the the answer for circumscribed?

Answer 11

not \[\sum_{k=1}^n\] but rather \[\sum_{k=1}^{30}\]

Answer 12

there are 30 rectangles so sum up to 30, not n.

Answer 13

replace k by 30 and you will see that you get the right hand endpoint

Answer 14

namely \[3(1+\frac{30}{15})^2=3(1+2)^2 = 3\times 3^2\]

Answer 15

inscribed just means use left hand endponts

Answer 16

what is the left hand endpoint?