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

Q: Find the area between the curves. x = -1, x = 1, y = ex, y = 3 - ex

A: We have to find the area between the curves : x=-1 ,x=1 ,y2=ex and y1=3-ex

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

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Q: Find the area between y=x+2 and y= x2−1. Round your limits of integration and answer to 2 decimal…

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Q: Set up a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x)…

A: f(x)=4-2x and a graph is given as shown below Formula Used : The Area of a f(x) in a given graph in…

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: Find the area of the region bounded by the X – axis, the lines x = 4 and x = 6 and the curve X – 1 A…

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Q: Consider the region bounded by the parabola y=4-x^2 and the x-axis. Set up a definite integral to…

A: Consider the following equation of curves: y=4-x2y=0 Points of intersection: 4-x2=0x2=4x=2,-2…

Q: 3. SET UP the definite integral that will give the area of the shaded region using a. y as variable…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other subparts as…

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: SET UP the definite integral that will give the area of the shaded region using a. r as variable of…

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

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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 the rectangles to approximate the area of the region. (Round your answer to three decimal…

A: Given that f(x) = 9 - x2 , [-3, 3] We have to find the approximate area by the rectangle given as…

Q: SET UP the definite integral that will give the area of the shaded region using a. r as variable of…

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Q: 4) Find the area of the region bounded by the curves y = 2x, y = sin x, x = 0, and a = Make 2 sure…

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Q: Sketch the region enclosed by the graphs of the given equations. Then, use a definite integral to…

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Q: Area inside the circle r = 3 cos 0 and outside the cardiod r = 1+ cos 0

A: The region which is inside the circle r=3 cos θ and outside the cardioid r=1+cos θ is:

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

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Q: Find an integral to represent the area of the surface obtained by rotating the curve x= (y - 2)3/2…

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Q: Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect to…

A: Let f(x)=y=x2      (1)g(x)=y=x          Compare x=x2x2-x=0x(x-1)=0x=0 or x-1=0x=0 or x=1Put value of…

Q: Show the set up of all definite integrals. Find the area of the region enclosed by the line y=2x-15…

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Q: Sketch the region whose area is given by the definite integral. - |x| dx 5. 4. 3 y 3 y 2 -4 -2 y 3…

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Q: Find the area of the region which is bounded by y = sin x - 3, y = 3x, y-axis and x = 2. Leave your…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Sketch the region enclosed by the curves y = (x-2)2 and y=x then find its area using the…

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Q: Find the area of the region enclosed by the curves y = 4 sin x and y = 4 sin 2x for 0sxST. y = 4 sin…

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Q: Set up the integral representing the area of the region between the curves * = :-2, x = 3, y=x²-3,…

A: We have to find value of area of shaded Region.

Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 3. Leave your…

A: Area bounded by the given curves :If f(x) and g(x) be two continuous function on a,b and f(x) ≥g(x)…

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…

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

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

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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 between the curves y = x and y = x². Area between curves =

A: It is given that,  y1=x and y2=x2 Therefore,                    x2=x⇒x2-x=0⇒x(x-1)=0 ∴  x=0,1…

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: Find the area of the region bounded by the x-axis and the curves y = 2 sin(x) and y = 2 cos(x) where…

A: First draw the graph of the both function and define the required area to be calculated.

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…

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Q: Let R be the region of the 1st quadrant surrounded by a curve. X : + 2 straight ine and straight 4 -…

A: We have to find the finite integral in first quadrant surrounded by the curve x=y^2+2 And the…

Q: Find the area of the region between the curves x 2y and x + y = 1. Area between curves =

A: Given curves are x = 2y2  and x + y = 1 Here we have to find the area between the curves.

Q: Find the area of the region between the graphs of y = 13 – x² and y = over the interval 3 < x < 8. –…

A: Solve by integration

Q: SET UP the definite integral that will give the area of the shaded region using a. x as variable of…

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Q: 3. Sketch the region bounded above by the curve y = x, below by the line y = -x - 2 and on the sides…

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Q: Find the area bounded by the y = x^2 + 5x and y = 3 − x^2 Sketch the curves and the region bounded…

A: The area bounded by the curves y=x2+5x and y=3-x2.

Q: Find the area of the region bounded by the curves: y=x^2+2x  and y=-x+4

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Q: 3. SET UP the definite integral that will give the area of the shaded region using a. y as variable…

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Q: ind its area using the appropriate definite integral

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Q: Find the area of the region bounded by the two curves:   y=6x+6 y=x^2+6   Set up the associated…

A: NOTE: Refresh your page if you can't see any equations. . given equations are to find the…

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: 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.

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.