finding area under curve using rectangles....

[sweetwater88]

These two questions have me stomped!

Find the area under the curve y = X^3 over the interval 0 < (less than or equal to) x < (less than or equal to) b (0<x<b) using either inscribed or circumscribed rectangles.

This one uses trapezoid rule. If the trapezoid rule is used with N = 5 then the intergal from 0 to 1 of dx over (1 + X^2) is equal to?

Any help?

 

[galactus]

What are your thoughts?. Show us some of your work and we'll see if we can help you along.

As for the previous post, the solid revolution, can you see how Soroban and I came up with the integrals?.

 

[tkhunny]

Re: Two questions need to be solved by midnight! Eastern tim

Find the area under the curve y = X^3 over the interval (0<x<b) using either inscribed or circumscribed rectangles.

What does that even mean? Is "inscribed" a lower bound rectangle and "circumscribed" an upper bound rectangle? Since y = x^3 is strictly increasing on the interval, the underestimating rectangles are always on the left and the overestimating rectangles are always on the right.