y =z² y = r³ - 12r Which of the following gives the shaded area? ........

Q: Find the area of the shaded region. y = JX - 3 (16,1) 16 (0,-3) Select one: A. 22 В. 38 3 O C. 16 D.…

A: Area of shaded region can be find as follows

Q: Q: Find the area of the region between the two curves yı=x? and y2=xt-12

A: Area between curves

Q: (f) Find the area enclosed between the line y = 3x and the curve y? = 25x. Calculate the area…

A: Only one question allowed to be solved at a time . I have solved 2 and included hints for third…

Q: = Which of the following represents the shaded area between y J(a) and y = g(x)! 8 6 2

A: We are asked to find which is represented for shaded area between the curves

Q: Find the area bounded by the indicated curves. y=6-6x, y=D0 The area is square units.

A: The given curves:y=6-6x2, y=0We need to find the area bounded by the given curves.

Q: Evaluate dw using the given information. 5x? + 4y? w = -; x= - 5, y= 3, z = 1, dx= 0.01, dy = -…

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Q: Q4. Ca) Graph s=2sin3 (b) Evaluate the area inside the curve.

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Q: y = g(x) - y = b ア=S(x) x = a

A: shaded area = area of rectangle- area between curve

Q: Find the area of the shaded region. y2 +x=2 y-x 0 f the following can be used to area of the shaded…

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Q: 3. 2 3. 4 7. To find the blue shaded area above, we would calculate: area Where: a = f(x) = %3D area…

A: Consider the given figure below :

Q: of the region in the first quadrant that is boun d below by the x-axis and the line y=x-2

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Q: Find the area of the region enclosed by the curves y=x²-3 and y = 1. The area of the region enclosed…

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Q: What is the area of the shaded region in the curve? -1 1 2 3 a. 0.7745 b. 0.4332 c. 0.8413 d. 0.3413

A: Here shaded area  P(z=1)-p(z= -1.5) Now probability p(1 <x< -1.5) Using Excel Function…

Q: d) Evaluate the area of the shaded region. y y =x'+1 -1 1

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Q: y= f(x) ) Estimate s and the left end points. S(2) dr with 8 recetangles

A: Part (c):-  Given integral is ∫08 f(x) dx Number of rectangle = 8 that is, n=8. So, step size = b-an…

Q: b) Find the area of the shaded region. 1) ii) y= T x=-y 2Fx= 2- y²

A: we have to find the area of the shaded region.

Q: Find the area enclosed by the x-axis and the curve y=4-x2. A 18 square units 32 B square units 3 ©…

A: topic - area under the curve

Q: Find the area of the shaded region. y x = y - 7 y = 1 x = ey -4 -8 -2 2 4 -6 y = -1 -2 -3 2.

A: We have to find the area with respect to y here. To find the area between x=e^y and x=y^2-7 we have…

Q: a of the shaded region is. to four decimal places as needed.) z= -0.92 z 1.29

A: Given The graph depicts the standard normal distribution of bone density scores with  mean= 0…

Q: Y(S) is given below. Calculate Y(t). 24 Y (s) = (s +2)(s+3)(s+4)

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Q: Kindly help

A: The area bounded by the curves are y = e2x, y = ex and x = ln 4 in the first quadrant.Use the above…

Q: B: Find the area of the shaded region show y y =1+x X=-1- y=-1 Fig(1)

A: According to the given below figure:  area of the shaded region is…

Q: B) 1. Graph the curve y = v3 – x2. 2. Find the area between the curve and the x-axis.

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Q: 20. Find the area of the shaded region for the function. 1 y = V4-x2 3- 2- * b. 똥 5T d. 3 a. е. 6.…

A: I take variable limits of y and constant limit of x

Q: Find the area of the region(s) enclosed by the curve (x) the x-axis, and the lines x = -1 and X= 2.…

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Q: Find the area of the region in the first quadrant that is bounded above by y = vx and below by the…

A: Given curves are y=x   .......1y=x-2    .......2

Q: Which of the following represents the shaded area between y = f(x) and y = g(x)? %3D

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Q: Find the area enclosed by the x-axis and the curve y=4-x². 32 A -square units 3 В 32 square units 36…

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Q: Find the area of the shaded region. 2 x = y? - 9 fy=1 x= ey -10 -8 -6 -4 -2 2 4 y= -1

A: This question is solved by concept of double integral.

Q: Find the area betwen the following curves.  x = -3, x = 1, y = x3 + 8, and y = 0.

A: Answer and explanation is given below

Q: Q. 2. Find the area of the region in the first quadrant that is bounded above by y = Vx and below by…

A: We will use double integration to solve the following problem.

Q: z = 0.62 The are of the shaded region is

A: Solution: Let Z be the standard normal variable with mean μ=0 and standard deviation σ=1. Z~N(μ=0,…

Q: y =  x2+3     y=11-x2 Find the area between the curves

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Q: 15. What is the area of the shaded region in the curve? -3 -2 -1 a. 0.7745 b. 0.4332 c. 0.8413 d.…

A: We have given that the shaded region in the curve.

Q: d'y and dx? dy 8) At which of the 5 points on the graph in the figure below are dx both negative?…

A: Points B and C which satisfy both the condition

Q: Ex6: Find for the foll dx a) x² y? = x? + y? 2 X-y c) - = 2 at P(3,1) x-2y Sol:

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Q: Find the total area of the shaded region. Ay 12 10- 8- 6- 4- y=x NO 2- Co y=7 y= 2 X 28 8 10 12 14 >…

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Q: Find the area within the curves y = 25 – x², 256x = 3y², and 16y = 9x². C. 36.27 units² D. 32.67…

A: In this question we have to find area within the curves

Q: Find the shaded region in the graph. y 2 +x soɔ = R/6 x/3 x/2 2/3 9/MG

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Q: Q3) for what values of (m) do the line ( y mx ) and the curve (y enclosed a region ? find the area…

A: There will be enclosed area only when both graphs cut each other at multiple points.  If graphs cuts…

Q: 25. Find the area of the curve r² = a²cos 20. B. a A. a² C. 2a D. a³

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Q: Find the area of the "triangular" region in the first quadrant that is bounded above by the curve y…

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Q: Find the area of the shaded region. y 2 x = y' -9 y= 1 x= e - 10 -8 - 6 -4 -2 4 Hy = -1 -2 2.

A: To find the area between the two curves f(y)=x=ey and g(y)=x=y2-9 Area between curves:…

Q: Q3/ Find the area of the region in the first quadrant that is bounded above by y = with respect to…

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Q: The graph of y = g(x) is shown below. The areas trapped between the curve and the x-axis are given.…

A: Definition used -                           ∫abf(x)dx=∫abf(u)du…

Q: Find the area of the region enclosed by the curves x+ y =0 and x+6y = 20. The area of the region…

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Q: The area of the shaded region: y-24 -1 (1.2) 2 3 5n

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Q: 01:42 d. Calculate the area enclosed by the curve y = 2x2 +3 and the x-axis between x = 0 and x 2.…

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Q: Find the area of the loop of the curve y? = r (4 + x) %3D Select one: O a. 34.02 sq units O b. 44.01…

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Q: y1=x2+2x+1 y2 =2x+5 Find the area of shaded region

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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.