Recent content by Niaboc67

@Svein I thought finding upper, lower and midpoints was essentially taking the partition {-3,-1,3} then breaking that into sub-intervals (-3,-1),(-1,3) then referencing the graph to see which is biggest or smallest in that interval. And in (-3,-1) if we are looking for upper that would be -1...

Homework Statement Find the upper, lower and midpoint sums for $$\displaystyle\int_{-3}^{3} (12-x^{2})dx$$ $$\rho = \Big\{-3,-1,3\Big\}$$ The Attempt at a Solution For the upper: (12-(-1)^2)(-1-(-3)) + (12-(-1))(3-(-1)) =74 For the lower: (12-(-3)^2)(-1-(-3))+(12-3)(3-(-1)) =42 For midpoint...

@Ray Vickson Has been corrected.

Homework Statement Find the area of the region between the graphs of: y=x^3+3x^2+5x and y = x^3+2x^2+7x on the interval [-1,2] The Attempt at a Solution I am not entirely sure what they mean by the REGION between the graphs, is this the region which encloses an area when the two functions...

Just want to see if I actually understand what these all mean. Partition: is like the x-coordinate values, also gives the number of times the graph was chopped up. We need them in order to find the distance or length of each rectangle. The distance is found by taking the further point minus...

That was how the question was defined. It said: let g(x) be any continuous function that satisifes -2x≤g(x)≤2x for 0≤x≤1. Find the upper and lower bounds for ∫[from 0 to 1] √(1+g(x)+x^2)dx Thanks

. Homework Statement Q1. Let f(x) be any continuous function that satisfies: $$-2x≤xg(x)≤2x$$ for $$0≤x≤1$$ Find the upper and lower bounds for: $$\int_{0}^{1} \sqrt{1+g(x)+x^2}dx$$ Q2. Let h(x) be any continuous function that satisfies: $$-4≤h(x)≤x^2-4$$ for $$0≤x≤1$$ Find the upper and...

My teacher mentioned this was a very important thing to know in calculus, he didn't explain too much about it but tried to emphasize how important is it. If $$P=\{a,x,...,x_{k-1},x_{k},...,x_{n}=b\} , P^*=\{a,x,...,x_{k-1},x^*_{k},x_{k},...,x_{n}=b\}$$ Then...

I got the wrong answer on my program. Wondering what I have done wrong in these calculations. Does anything stand out?

Mod note: Merged a separate thread with this one 1. Homework Statement Let, f(x) = x^2 and let P = { -5/2, -2, -3/2, -1, -1/2, 0, 1/2 } Compute Lf (P) and Uf (P). [f] (P) = U[f] (P) =The Attempt at a Solution I followed the pattern of distance times height. Therefore the further number in...

@PeroK after graphing it seems fuzzy to understand this problem and what I must do.

@PeroK I understand. Just this problem confuses me. I don't know how to even approach solving.

@PeroK I wish I knew. This problem seemed to be either worded weirdly or just isn't providing enough information to solve. Don't I have to take the 6 partitions and then take only the first number in the partition subtracted by the last number in the partition and divide by those two numbers by...

@PeroK ok nevermind I got two different questions mixed up there. Really unsure how to even go about solving this problem. Could use a push in the right direction.

Homework Statement Let f(x) = x^2 and let P = { -5/2, -2, -3/2, -1, -1/2, 0, 1/2 } Then the problem asks me to compute Lf (P) and Uf (P). Lf (P) = Uf (P) = The Attempt at a Solution Please explain how to solve. I thought that L[f] meant to calculate the lower bound with respect to f(x)...