a single integral whose value is the area of the region bounded by the curves y = 12−x^2 and y = x^2 − 6

Q: Find the area bounded by the graphs of y = 4- x^2 and y = x - 5 between x= 0 and x= 2. Sketch the…

A: Given query is to find the the area of region bounded by the curves.

Q: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

A: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

Q: Find the area bounded by the curve x = (y+1)2 and y+1 = x2. Show complete solution of points of…

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Q: The region is bounded by x+6=0 and y^2+x+2=0 is revolved about x=-6. find the integral in finding…

A: Consider the provided question, The volume for solid of revolution between the curves x+6=0 and…

Q: Find the area of the region enclosed by the curves y - 2x =7 and x - y= 4. Set up the integral that…

A: Answer and explanation is given below..

Q: An oil leak from an uncapped well is polluting a bay at a rate of ƒ(t) = 125e-0.025t gallons per…

A: An oil leak from an uncapped well is polluting a bay at a rate of ƒ(t) = 125e-0.025t gallons per…

Q: The region of integration for the double integral of f(x,y) is given by 0 < x< 1, y = e*, and line…

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Q: region bound by y=x2 y=2x and y=3, rotated about x=-1, set up the integral using washer method,…

A: Graph the bounding region and the axis of rotation. Since the axis of rotation is a vertical axis,…

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A:

Q: 2) y=x y=4-3x 21

A: Given:   Curves y=x4 and y=4-3x2   We start finding their point of intersection.        x4=4-3x2…

Q: Find the area of the region in the first quadrant bounded by the curve (x + 2)² y = 4 – x. [Use the…

A: Given that: (x+2)2y=4-x

Q: With y > x > 0, find the area of the region between the y: curve, x = 0 and x = y lines %3D with a…

A:

Q: Find the area of the region bounded by (enclosed by) y = x² + 5x and y = 5x + 4 Be sure to a) graph…

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Q: . The region is bounded by X = y² and x = 4(y − 2)² Using horizontal rectangles, set – up the…

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Q: Use double integral to find the area of the region bounded by the lines y = x – 2, y = -x, and the…

A: Solution -

Q: 2) y =x ya 4-3x

A:

Q: What is the integral expression of the area of the region bounded by the curves x= y - y^2 and x =…

A: Area between curves

Q: Find the area of the region bounded by the curve y=x²-3x²-x+3 and x-axis from x=-1 to x=2. (Note:…

A: To find the area of the region bounded by the curve y=x3-3x2-x+3 and x‐axis from x=-1 to x=2.

Q: Calculate the total area of the region described. Do not count the area beneath the X axis as…

A: Given: Bounded by the curve.y=1-x2And the lines x=-1 and x=2

Q: The curves x = 4y - y^2 and x = 2y - 3. Set up a single integral that evaluates the shaded area and…

A: Given  x=4y-y2 ,x=2y-3  To find  Area between  given curve using single integration method

Q: Sketch the graph of the curve y z (x-6)(x-7)(x-8) Shade the area of the region bounded by the curve,…

A:

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: the area is given by A=∫ab|fx-gx|dx here we have fx=7x g(x)=0 a=0, b=16

Q: The definite integral that calculates the area of the region enclosed by the curves y=4 - x² and y =…

A: Solution of the problem as follows

Q: The region R is bounded by the curves x = y^2+2, y = x-4, and y = 0. Write a single integral that…

A:

Q: Find the area bounded by the curve y = 2x + x² – x³, the x-axis and lines x = 0 and x = 1. %3D

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Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: The green region is the positive region while the blue region which is below the x-axis is the…

Q: Find the area of the region bounded by the graphs of the equations                y = 6x2 / (x3 − 2)…

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Q: Decide whether to integrate with respect to x or y. Find the area of the region.   6x+y2=16,   x=y

A: here we have a y2 term so we will  integrate with respect to y the first equation is 6x+y2=16…

Q: The area of the region bounded by the curves y=x and y= 20–x² is 5 A = I120-x²-x| dr -4 »4.4…

A: Given, The curves y =x  and y=20-x2  We have to find the area of the region bounded by the curves.

Q: Sketch the region of integration for the double integral given by integral 0 to ln2,e^x to 2 dydx…

A:

Q: Express the area of the shaded region in terms of an integral (or integrals). Do not evaluate your…

A: Given,

Q: Sketch the graph of the curve y (x-p)(x-p-1)(x-p- 2) Shade the area of the region bounded by the…

A:

Q: Calculate the area of the region R enclosed within the following boundaries: x² + (y – 1)² < 1 y <x…

A: (a) Here we first plot the given curves and then find the common region bounded by all curves. (b)…

Q: Use an iterated integral to find the area of the region bounded by the graphs of…

A: We have, f and g are given as function of x, thus a vertical representative rectangle is convenient…

Q: Sketch the region bounded by the graph of y= (½)x² + 1 and thex-axis between x =--2 and x= 4. Set up…

A:

Q: *** By using horizontal element, the definite integral representing the area of the region bounded…

A: Given, x=y2, y=1 and the y−axis   The shaded region is

Q: Find the area of the region bounded by the curves y = 2x°, y = 5x + 6, x = 0. Set up the integral(s)…

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Q: Sketch the region enclosed by the curves: y= x^2-1, y = 7-x^2. Then set up (but do not evaluate) the…

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Q: Sketch the graph of the curve y = (x – 7)(x – 7 – 1)(x – 7 – 2) Shade the area of the region bounded…

A: In the graph, the horizontal axis is x-axis and the vertical axis is y-axis. We need to find the…

Q: Express the area of the shaded region in terms of an integral (or integrals). Do not evaluate your…

A: Firstly, we need to calculate the points of intersection of th given curves…

Q: Sketch the region of integration for the double integral given by integral 0 to ln2and e^x to 2 dydx…

A:

Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0, using a vertical element.…

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Q: A gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 15 ft and…

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Q: Find the area of the region bounded by y=x²-1, x=2 and y=0. Use horizontal element and express area…

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Q: By using horizontal element, the definite integral representing the area of the region bounded by x…

A: To calculate the area of the region first obtain the bounds of the region. This can be done by…

Q: Sketch the region bounded by the graphs of the functions and find the area of the region y = x³ – 4x…

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Q: Consider the region formed by the curves y = 2x² – x +1 and y = x² + x + 4. a. Compute for the end…

A: Let's find.

Q: The shaded region in Figure 2 is bounded by the curve y=8-x², lines y=7x and y=2x. Set up the…

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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.