Find the area obtain when the curve f(x) = x² – In æ, for 1 < x < 3, is rotated about the y-axis.

Q: Q:: Find the area bounded by the curve Vx+/y = 1 and the coordinate %3D axes, at x = 0,and y = 0

A: lets assume a horizontal strip under the region boundedwe get0≤x≤(1-y)2 0≤y≤1

Q: Find the area bounded by the given curves. 1. x^2=4y , 3x-4y+4=0

A: The area between the curves is the area between a curve fx and a curve gx on an interval a,b given…

Q: Consider the function f (æ) = –x² + 9. What is the left rectangular approximation of the area under…

A: Given:       fx=-18x2+9    Interval -6,6 with 6 equal sub intervals.   The left rectangular…

Q: Solve the area covered by the x-axis and f(x) = e^x from x= 1 to x = 4 with interval h = 0.25 using:…

A: ∫abf(x)dx≈Δx(f(x0+x12)+f(x1+x22)+f(x2+x32)+⋯+f(xn−2+xn−12)+f(xn−1+xn2)) Mid point rule and…

Q: (b) Find the area enclosed by the curve y = 4x2 and the x-axis between x = -2 and x = 2. %3D

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Q: Find the area under the curve y = f(x) over the stated interval.

A:

Q: What is the total area of the curve y T and the x-axis between I =1 and x = -1? %3D -1

A:

Q: 1. Find the area bounded by the curve y In x and the %3D lines y = 0 and x = e.

A: Given curve is: y=lnx and the line y=0 and x=e Area of bounded regions: Let y=f(x) be a continuous…

Q: A Find the area bounded by y = e*, y = xe*² & x = 0.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find the area bounded by the curve r2 8 cos 0. %3D

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Q: - y = x' 3 from x=-1 to x=2 %3D

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Q: a) calculate the area of the area bounded by the Curves 4= Sin 2x and y =Sin 2x, 0s;

A: Hello, thanks for your question but according to our policy I can only provide the typed answer.…

Q: Find the area enclosed by the curves y = sin x y = cos x from x = 0 to x = T. and

A:

Q: 3.) Find the area bounded by the curve y? = 2x and y =x-4 a.) Using Vertical strips b.) Using…

A: Given: The equation of the curve y2=2x andy=x-4. to find the area bounded by the curve using…

Q: Find the area bounded by the curve x=3+cosØ, y=sinØ

A: the given curves are x=3+cosϕy=sinϕ

Q: Find the area between y = ex and y = e2x over [0, 1].

A:

Q: The area bounded by the curve x = 3y + 8, the y- axis and the abscissas y = 0 and y = 2 is O 19 O 1…

A:

Q: Use the Right Rectangular Approximation Method with n=2 to approximate the area under the curve of f…

A: Given function :   Integration of function gives area under the curve.

Q: Calculate the area contained between the curve y = cos x, π<x< , and the line y =

A: Given:-y=cosx, -π&lt;x&lt;πy=1/2

Q: Find the area under the curve y 12 over the interval [ – 1, 1]. %3D (x + 2)² area = i

A:

Q: 3. Find the area bounded by the curve 2x? + 4x + y = 0 and y = 2x. %3D Answer: 'n 'bs

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Q: B) Determine the net area for y on the interval %3D

A: Here is the solution:

Q: Let r(t) = (sin(2t), sin(t)) for 0<t<T. Find the area bounded by this curve, rounded off to two…

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Q: Find the area under the curve y = 18 - over the interval [ – 1, 1]. %3D (x + 2)? area = i

A:

Q: The area enclosed by the curve r = 3cos30 is

A: Given curve is that, r = 3cos3θ we have to find the area bounded by given curve.

Q: Use the Trapezoidal Rule to approximate the area under the curve ƒ(x) = 3x² x on the interval [2,…

A:

Q: Find the area obtain when the curve f(x) = x² - In x, for 1 <x< 3, is rotated about the y-axis.

A: Given Data The equation is f(x)=x²-1/8lnx. The interval is 1≤x≤3.   The equation of the area of the…

Q: 3. Find the area bounded by the curve 2x? + 4x + y = 0 and y = 2x. Answer: sq. u.

A:

Q: Q6) Find the Area bounded by the curves y = √√√x and x = 2y - y² ,with sketch.

A: Let's find area between two given curves.

Q: Find the area under the curve y 24 over the interval [ – 1, 1]. (x + 2)? area = i

A: By Solving area under curve

Q: 2y = x, x = 0, and y = %3D

A:

Q: Using the fundamental theorem, find the area under the curve y = 4x3 −2x+5 and above x-axis on the…

A: Fundamental theorem: To find the area under the curve y=f(x) between x = a and x = b, simply find an…

Q: Find the area enclosed by the curve x = t2 − 3t, y = Square root of t

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Q: Find the area between y = e" and y = e3² over [0, 1]. A =

A:

Q: Find the area between y= e" and y = e over [0, 1]. %3D A =

A:

Q: Find the area between the curves f(x) = tan (x)sec (x) and y = 0 between r =0 and r = .

A: Given curves are

Q: Determine by direct integration the second moment of area about the x-axis [units^4] of the area…

A:

Q: Find the area of this region using the Fundamental Theorem of Calculus: 2+cos x dx

A: Consider  ∫0π2+cosxdx

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

A: Riemann sum

Q: Find the area obtain when the curve f(x) = x² - In r, for 1 <a< 3, is rotated about the y-axis.

A: The area obtained when the f(x) is rotated about the y-axis is given as: where a is the lower limit…

Q: Find the area under the curve y 2 I over the interval [1, 4]

A: Find the area under the curve y=2x over the interval [1, 4]

Q: Q2) Find plane area bounded by functions y = x,y 3,and x = 5.

A: We have to find the area bounded by the functions: y=x, y=3, and x=5For y = 3 we have x = 3

Q: Find the area under the curve f(1) = r' o I = [– 0.5, 4.5] using the M %3D

A: Introduction: The formula for the mid-point rule for a continuous function f(x) on a,b is given by,…

Q: Write the integral used to evaluate the surface area when the given curve is rotated about the…

A: The objective is to write the integral used to evaluate the surface area when the curve is rotated…

Q: Find the area under the curve y = -over the interval [0, 4]. (2x + 5)2 Enter the exact answer. area…

A: Find your answer below

Q: A Find the area bounded by y = e*, y = xe* &x = 0.

A:

Q: B- Find the area under curve y= (e*/x )dx from x=0 to x=4. use midpoint method with n=4

A: By Midpoint Rule:

Q: Q2) Find plane area bounded by functions y = x,y = 3,and x = 5.

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.