Find the area bounded by the graphs of the indicated equations over the given interval. y=x2 - 21; y = 0; - 3sxs0 The area is square units.

Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: 2x2+4x+4 Estimate the area of the curve y = 2 from x = 1 to x = 3 by using 5 rectangles and right…

A: We find out the area of given curve usin Rieman sum where dalX=(b-a)/n where n is the number of…

Q: Find the area to the left of z = -1.5 Solution: Dr sh

A: P(Z<-1.5)=?

Q: - A. Find the area enclosed by y = 5x – x² and y = x. Solve and Draw. 1

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Q: Find the area bounded by the graphs of the indicated equations over the given interval. y = - 4x +…

A: Area bounded by the curves  y = -4x + 12 and y = 20 where x is in between -1 to 2

Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 3. x-…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find the area enclosed by the x-axis and the curve y=9- x². 32 square units 3 A B 36 square units 32…

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Q: Find the area between the graph of the curve y=x√(1 + 2x2) and the x-axis over the interval…

A: To Find: The area between the graph y=x1+2x2 and the x-axis over the interval 1,2. Concept: Area…

Q: x² +1 dx x'(x-1)² 3

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Q: Find the total area between the region and the x- axis. y = x3 – 3x? + 2x -1 sxs2

A: Consider the curves, y=x3-3x2+2x  ;       -1≤x≤2

Q: Find the area enclosedby the parabola y=x² - 8x+15 and thex-axis.

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Q: x2 – 7x + 20 and Find the area of the region bounded by the graphs of the functions y = y = 2x + 6.…

A: Given, Functions  y =x2 -7x+20  and y =2x+6 We have to find the area of region bounded by the graphs…

Q: D. Graph each of the given functions and solve for the area of the region that they enclose. 2. 4.…

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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 enclosed by the parabola y=x2-8x+15 and the x-axis

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Q: Find area bounded by the circle x? + y² = 25, the y-axis and the parabola y = 6x – x².

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Q: ƒ(x)=3x² +6x−9

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Q: C. Solve the following problems Find the area bounded by the curves y = 2x and y? = 4x about the…

A: As per the bartleby guidelines we only give first question answer.

Q: Find the area A of the region between the graphs of the equations y? = 9x x2 = 9y A = 27 9.

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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: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - r, and the line perpendicular…

A: Triangle bounded by the y-axis, the line f(x)=5-(x/7) , and the line perpendicular to f(x) which…

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: D. Graph each of the given functions and solve for the area of the region that they enclose. 2. 4.9…

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Q: Homework Q40. Find the area bounded by the curve y = 3x² + 14x +15, the x axis and ordinates x = -1…

A: Desired Area

Q: Sketch the figures and show step by step solutions. Find the area between the curve y = x3 – 6x2 +…

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Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 2. The area is square units. ...

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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: walk through this problem

A: Let's understand the area enclosed. Please see the diagram below: f(x) = x2 / 2 + 1; g(x) = x2 / 2 +…

Q: Find the area of the region bounded by the x-axis and the curve below (Show all steps). y = 3x° +…

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Q: Find the area, take the elements of the area perpendicular to the x-axis. x²-y+1=0; x-y+1=0.

A: Given, x²-y+1=0 I.e, x= sqrt(y-1)----- equation 1 x-y+1=0 I.e, x= y-1 ----equation 2

Q: 11. Find the area within the curves y 25-x', 256x=3y², and 16y = 9x². A. 37.26 units? B. 37.62…

A: Given the curves  y=25-x2 ,256x= 3y2 , and 16y=9y2 Determine the area within the given curves

Q: Find the area of the shaded region. Show your complete solution. r = 0

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Q: a) Find the area of the curve x²/3 +y2/3 = a²/3 %3D

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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 area bounded by the graphs of the indicated equations over the given interval. y =x - 19; y…

A: First I have written a short note about area between two curves , just use them for the given curve…

Q: Find the area bounded by the indicated curves. y=2x, y 6-4x, x= 0 (x20) The area is square units.…

A: topic - area bounded by curves

Q: Find the area of the region bunded by the graphs of the given equations.     y= 2x+15 y=x^2…

A: Given Data: Equation 1: y=2x+15 Equation 2: y=x2 The figure below indicates the area bounded by the…

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 bounded by the curve y=-x³x² + 3x and the line y=x. 16 A 8 square units B 16 square…

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

A: We have to find the area

Q: Find the area bounded by the graphs of the indicated equations over the given interval. y=x2-16; y=…

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Q: Find the area between x2 = -2y + 8 and the x - axis.

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Q: 3. y = x2 + 5x and y = 3 – x -

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Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 3. The area is square units.

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Q: Sketch the figures and show step by step solutions. Find the area lying above the x-axis and under…

A: We have to find area for given curves.

Q: Find the area bounded by the graphs of the indicated equations over the given interval. y=x* - 23; y…

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Q: Find the first quadrant area bounded by the circle x? +y² = 25, y-axis and the parabola x2 – 2x = y.

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

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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.