Question

Solve using 10 circumscribed rectangles of equal width (an upper sum) to estimate the integral from 0 to 1 of x squared, dx.

Answer 1

You need to draw the graph from 0 to 1 and separate it in to 10 segments, all with equal width (width of 0.1), measure the corresponding height, calculate the area for each specific square and then add all the areas together, as depicted in the above pictures.

Answer 2

is there a formula or anything like that i can use?

Answer 3

You can use the right endpoints of the subintervals.

Answer 4

There are ten subintervals from 0 to 1.
Delta x = ( 1- 0)/10 = 0.1

Upper Sum = .1 * f(.1) + .1 * f(.2) + .1 * f(.3) + ... + .1 * f(1.0)
= .1 * .1^2 + .1 * .2^2 + .1 * .3^2 + ... .1 * 1^1

Answer 5

would i go to nine or ten?

Answer 6

there should be 10 terms

Answer 7

so i would do .1 times 1^2.... and so on until theres ten terms and then would that give me my answer

Answer 8

There are ten subintervals from 0 to 1.
Delta x = ( 1- 0)/10 = 0.1

Upper Sum = .1 * f(.1) + .1 * f(.2) + .1 * f(.3) + ... + .1 * f(1.0)
= .1 * .1^2 + .1 * .2^2 + .1 * .3^2 +
+ .1 * .4^2 + .1*.5^2 + .1*.6^2 + .1*.7^2 +.1*.8^2
+ .1*.9^2 + .1*1.0^2

Answer 9

.385?

Answer 10

Okay i have another problem similar to this one