Integrals Resources

Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a).   Hint: Use the Mean-Value Theorem. (Recall that, if P...

Lets say, I  have a cube with with Volume = a*a*a. I also have a sphere (hole) with coordinates X,Y,Z and radius r in the cube. My task is to slice the cube (perpendicularly to Y), when each...

The question asks to estimate the area under the graph given the following table: | x | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 | | y | 4 | 10 | 8 | 6 | 14 | 10 | 12 | a) Use Simpson's...

I got the answer to this problem from my teacher but I don't understand why that's the answer: y=√1+x^3 , domain 1≤x≤2 and with 50 intervals therefore width is 1/50.  The Sigma notation...

I need to form a logo using functions and then find the area of the logo but I don't know how to. The summary of the question is the direct question. Some logos we can choose from are the xbox...

What is the value to 2 decimal places of the following integral when a = 12, b = 32, c = 1.1 and d = 5? \int_a^{^b}\left(\frac{c}{x}-d\left(\sin\left(x\right)\right)\right)dx