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...

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...

Calculate the area of the region bounded by the two curves, y = 4 - x2 and y = x + 2. The answer is meant to be 9/2 but I just cannot get it!!! Maybe my bounds are incorrect......

a) 87.75 b) 15.75 c) 11.25 d) 6.75

Estimate the integral ∫15(top)3(bottom)(−x2+0.07x−0.9)dx using a right Riemann sum with 6 subintervals.

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...

I have been stuck on this integral for 3 hours. Here is what I have so far.. : https://ibb.co/mWAC7x

∫dx/(x+1) - ∫dx/(x+2) = log| (x+1)c/(x+2) |

I feel that there should be another x in the problem so that u sub works, or something, as it is I believe it is a partial gamma function or something, but I know we should not learn those until much...

The function to be integrated is the following: f(x)=(√x)/(x2 + ln(1+x)) In addition to this we were asked to confirm if the function converges or not. When plotted it is...

∫10−10|x|dx∫−1010|x|dx =

Calculate the integral below, assuming that ∫50f(x)dx=5∫05f(x)dx=5 and ∫50g(x)dx=12∫05g(x)dx=12. ∫50(6f(x)−13g(x))dx=

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 was asked to calculate the area between two functions, y=e^x and y=x using midpoint riemann sums from 0-2 with n=4. so i found my answer by subtracting the second sum from the first. The second...

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...

integral cccalculus with respect to dx

The answer which I got was (e^(-x))sin(x/2)-cos(x/2)(e^(-x)) However all the math solvers on the internet are giving different answers. Could you clear things up and tell...

Water flows into a reservoir at a rate of 1500 + 7t2 gallons per hour. since there is a tiny hole in the reservoir, the water leaks out at a rate of 4t + t2 gallons per hour. What is the net...

Find the integral of sec2(x)tan2(x)dx

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

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