find the Curve A the region enclosed by ye Sin (ITx/2) and the the area line

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be

Q: Determine the area of the given region under the curve.

A: see the attached file for a detailed solution.

Q: of the region y=lax, Find the area bounded by the y=x-1, yi-2. curves

A: I have provided solution in  step2.

Q: Find the area of the region.vo Total area bounded by the curve r = sin 20

A:

Q: Find the area between the curve y = -x< + 6x – 8 and the x-axis from x = 2 to x = 4. (Give an exact…

A:

Q: Approximate the

A: Given,

Q: Sketch the region bounded by the given curve. Then find the area of the region. y=3+2x-x^2, x-axis

A: y=3+2x-x2 The graph is,

Q: Sketch the region bounded by the curves and find the area of that region.

A:

Q: obove y=O Exampe: Find the area under the curue and to the right of - x=

A: We have to find the area in this question.

Q: Find the area bounded by these curves

A:

Q: 5. x = 8 – y², x = y² – 8

A: This question is based on application of definite integral.

Q: Find the area of the region enclosed by one loop of the curve r = 4 sin(7theta)

A: Loop:- A curving or doubling of a line so as to form a closed or partly open curve within itself…

Q: Approximate the area under the curve y

A: Introduction: The formula of the trapezoidal to approximation is given by,…

Q: Iwo curves having an equation of x = 2Vy and Compute the area between the two curves.

A: Given,          x=2y    and    y=2x

Q: Approximate the area under the curve y = x° from x = 0 to x = 3 using a Right Endpoint approximation…

A: The given curve is

Q: Find the area of the region R bounded by y-3-x and coordinate axes.

A:

Q: Find the area bounded by the curve y=x^3 -3x and the x-axis. Sketch the curve that are bounded

A:

Q: Find the area bounded by: x^2 + 4x + y =0 and x + y = 0. Draw the curve and label the graph.

A: Given, x^2 + 4x + y =0 and x + y = 0.   or y=-(x2+4x) and y=-x

Q: Determine the area of the region enclosed by y=sinx and y=cosx, x=π/2 and the y- axis .

A:

Q: Find the area of the region bounded by one loop of the curve y"(1 - у?)

A:

Q: find the area bounded by the given curve y=2x-x^2 and y=

A: The area bounded by the two curves is given by ∫abf(x)-g(x)dx where f(x) and g(x) are two curves on…

Q: Approximate the area under the curve graphe

A: answer is in next step

Q: Sketch the region enclosed by x + y x + y = 0. Decide whether to integrate with 6 and respect to x…

A:

Q: Sketch the region enclosed by the given curves. y=5cospix, y-12x^2-3 Find its area.

A: Plot the curves. From curve, upper curve=5cosπxLower curve=12x2−3LL=−0.5 and UL=0.5

Q: Sketch the curve. r = 4 - sin(0)

A:

Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: Approximate the area under the curve y x from = with 6 subdivisions. 5 using a Right Endpoint…

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Q: Sketch the region enclose by the curves and compute its area as an integral along thex- or y-axis. x…

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Q: Sketch the region enclosed by the curves and find its area. y = x, y = 3x, y = -x + 4

A: Given; y=x, y=3x, y=-x+4   Now find the point of intersection between the line y=-x+4 &amp; y=3x.…

Q: Sketch the region enclosed by the curves y = - 1+x2 and y = 5 – |x|. Find its area.

A: given curves are                                        y=-31+x2 and y=5-|x|

Q: Sketch the region bounded by the graphs of y= 1 divided by x7 , y=0 , x=2 , x=5. Then compute the…

A: area bounded by   curve...

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The given curves equations are     2y=4xy=32y+2x=6

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: zty xydx dz dy

A:

Q: Find the value of a and b if the curve +b) touches the x-axis at x=2 and line y=2x at the origin.…

A: Given curve is y=x(x-2)(ax+b) The curve touches x-axis at x=2 and the line y=2x at the origin. The…

Q: Sketch and find the area of the region below the interval -3, -2 and above the | curve y = . Area…

A: An interval is given by -3,-2 and a curve is given by, y=x34  . The objective is to sketch and find…

Q: Calculate the area under the ROC curve. Interpret what this area means in words in the context of…

A: We have the provided data as Where Xk (1- Specificity) and Yk (Sensitivity) represent the…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y…

A: Let's find area enclosed by given  curves.

Q: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

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Q: Find the area of the region bounded by : Sketch the graph.

A: To find: Area between the curves:

Q: Estimate the area under the curve from x=0 to x=5 using 5 approximating rectangles and left endpoir…

A: In this question, the concept of Riemann Sum is applied. Riemann Sum To estimate ∫abfxdx, Riemann…

Q: Sketch the region bounded by the curves y = sin(x) , y = cos(x), 0 <x <I and evaluate the area.…

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Q: Find the area of the region between the curves

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Q: Calculate the area of the area between the curves

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Q: Find the area between the curve y - x + 9x + 20 and the x-axis from x - -4 to x - -2. (Give an exact…

A: Given, y = x2 + 9x + 20  x = -4 and x = -2  We have to find the area of between the curve y = x2 +…

Q: Find the area bounded by the given curve and lines. y = x3,y = 8, and x = 0 %3D

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Q: +4

A:

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: how do I determine the area under a curve?

A:

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.