Question

Can someone show me how to use the Midpoint Formula with n = 5 to find integral from 1 to 0 of (1+x^3)^1/2dx

Answer 1

\[\int\limits_{0}^{1} \sqrt{1+x^3}dx\]

Answer 2

i know that the graph
and that delta x = 1/5

Answer 3

\[
\Large
\sum_{i=0}^{5-1}f(\overline{x_i})\Delta x
\]

Answer 4

Where\[
\overline{x_i} = \frac{x_{i+1}+x_i}{2}
\]And \[
\Delta x = \frac{b-a}{n}
\]

Answer 5

And \[
x_i = a+i\Delta x
\]

Answer 6

\[
a = 0 \\ b = 1 \\ n = 5
\]

Answer 7

You already have \(\Delta x\). so just make a table of your \(\overline{x_i}\)

Answer 8

Then make a table of \(f(\overline{x_i})\).

Answer 9

@jennychan12
Not really that challenging, just a lot of work.

Answer 10

the midpoints of each subinterval from 0 to 1 is:

find the x-coordinate of all those x's and plug into f(x) to get the height of each rectangle.
the width of each rectangle is 1/5.