'Find the area enclosed by the following points using: Simpson's Rule 2 4 8 14 18 21 f(x) -3 -1 4 6. 7 8 12

Q: Find the surface area of the portion S of the cone z² = x² + y², where z ≥ 0, contained within the…

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Q: #7. Describee the area represntecl by lin in n-1

A: L'Hospital's rule:

Q: 20) The Taylor series for the function F(x) = S e¯ dt is E(-1)"n(4n+1) z4n+1 all x E R. n=0 a) True…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: 3. Using a substitution, show that the following shaded areas are equal. You do not need to compute…

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Q: Given the area of each region denoted by A, B,C, and D. A = 27 B=3 C - 16 D=6 C (-3,0) (5,0) B…

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Q: в х3 - 4х (3,15) (0,0) 17 В) 33 C) 4 41 A) D) 3.

A: since area below x axis is negative therefore we need to take the absolute value of the area of the…

Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: Evaluate the area bounded by : * 3+y x = 1+ Jy,x = 3 7/s square units / square units % square units…

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Q: (2) Find tume area of reason borunded by the graphs of tue equations d-**, the M = I, x=3,and Pound…

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Q: 2. Find the area of the region bounded byx = 4y – yʻ, and x =y. -2+ 15 A) square units 2 C) square…

A: The area under the curve is obtained by using double integration I=∫ab∫f(x)g(x)dydx or…

Q: Let A be the region enclosed by y =1/√x, y = 0, x = 16, and x = 25. -Write an expression for the…

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Q: Find the area of the shaded region. 5:3 1 23 ex - 3>2 (2,1) (4,1)

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Q: 10) Find the area of the shaded region. 6x 7x- 2- 5x -9 8x + 4

A: To find the area of the shaded region in the given figure Dimensions of the outer parallelogram…

Q: Find the sccond derivate Of the finctron Y =2*. Inx

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Q: ... 10 10 What is the area of the region bounded by the parabola y = 10 – x², y – axis, x – axis,…

A: We have to find the area bounded by the curve

Q: 3. Let U be the domain inside the square |x + y = 4 and outside the circle x² + y² = 1. Use Green's…

A: Given that the domain inside the square x+y=4 and outside the circle x2+y2=1.

Q: Find the surface area of the portion S of the cone z² = x² + y², where z ≥ 0, contained within the…

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Q: a. Using three approximating rectangles and midpoints, find the approximate area under the curve of:…

A: The given function  , The midpoint rule

Q: Find the area bounded by the curvey = x², the x-axis, and the ordinates x = 1 and x = 3. (no need to…

A: Topic = Area Question no 2 and 3 are graded questions.  Only question no 1  can be answered.

Q: y y = flx) 4 8.

A: Given,fx is a decreasing function Left endpoint gives upper estimateRight endpoint gives lower…

Q: Use the surface area formula SA = /I. V1 + f% + f; dA to prove that the surface area of the sphere…

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Q: 1. Egor rode his skateboard for 12 seconds- see the figure below. Egor's Skateboarding Adventure i)…

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Q: 16. Find the area of the region. -2,4 f2,4) 2- y=x-3x -2

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Q: What region R in the xy-plane minimizes the value of the following expression? JS (2² (x² + y² - 9)…

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Q: are going to find the area of some trapezoids using the rule - x (side a + side b) x height h 6 mm…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.