Find the area under the graph of f(x) = 4¬3# and above the graph of f(x) = 0 for æ in [4, 6] by integrating.

Q: Evaluate the integral. (Use C for the constant of integration.) | 16 In(V) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 3 dx x(x4 + 5)

A: In this integrated we will assume x4 =t , then we will solve it

Q: Find the area bounded by the parabolas x2+y-9=0 and x2-8y=0   (SOLVE BY USING INTEGRAL CALCULUS)

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Q: Evaluate the integral. (Use C for the constant of integration.) x5 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 [BX 8x √√x + c dx

A: Given ∫8xx+c5dx

Q: 2 S (x) + x³)dx = ? -1

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Q: Evaluate the integral using tabular integration by parts. (3 x² – x + 1) e¬¤ dæ +C -

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: dx XV 16x4 – 1

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Q: When using a change of variables u = g(x) to evaluate the definiteintegral, how are the limits of…

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Q: evaluate the double integral ∫01∫y1 √1+x2 dxdy by changing the order of integration

A: In this question we will use basic of calculus i.e concept of double integration. We will change the…

Q: Evaluate the integral. (Use C for the constant of integration.) 7x2 + x + 7 dx (x² + 1)2

A: The given integral is: ∫7x2+x+7x2+12dx To evaluate the given integral.

Q: Below is the graph of y=z3 and y =0 0.5 -0.5 0.5 1 -96 -1 (a) The area bounded by y=z3 and y 0 is…

A: One area is from -1 to 0, other is from 0 to 1 For the area -1 to 0, the curve is below the x-axis.…

Q: x³ + 4 dx x (x+1)

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Q: (4A)Find area bounded by y = 0, y =√x-x² using double integration.

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Q: Q4A) Find area bounded by y = 0.y = √2x-x² using double integration.

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Find the integral xn ln x dx; n ≠ −1, n real. (Use C for the constant of integration.)

A: we have to use integration by parts ∫uvd=u∫vd-∫du∫vdd  and ∫xndx=xn+1n+1+c where c is the…

Q: I. Find the area bounded by the curves y=x', y 1, and x = 0 using double integration.

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Q: Evaluate the integral. (Use C for the constant of integration.) (1.2^x+4^x)dx

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Q: Use numerical integration to estimate the value of 1 dr. 1 + x TT = 4

A: Given: prove that π=4∫0111+x2dx  for proving this we will solve right hand side  we know that…

Q: Find the area bounded by the y-axis and x = 4-y2/3 (Solve using Integral Functions)

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Q: Sketch the region of integration corresponding to y²e= drdy, (log æ)3 J = and evaluate J.

A: We will evaluate the given integral.

Q: Evaluate the integral. (Use C for the constant of integration.) dx

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Q: x-3 dx r³+9x +9.x

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Q: Evaluate the integral. (Use C for the constant of integration.) x + 21 dx x + 20x + 104

A: Consider the provided integral, ∫x+21x2+20x+104dx Evaluate the provided integral. Apply the…

Q: Evaluate the integral by reversing the order of integration 4 16 2 dy dx 3 ys 1 0 х In(48) X

A: The given integral is,

Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 21 dx 3x + xVx + x/x

A: Explained below

Q: Evaluate the integral. (Use C for the constant of integration.) 7 dx x(x* + 1)

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Q: Evaluate the integral r4-x2 8x cos y dy dx r2 y – 4 by reversing the order of integration.

A: Evaluating the g8iven integral directly is not easy. So if we change the order of integration from…

Q: If f(x)dx - + what are the bounds of integration for the first integral? a = and %3D

A: To find the bounds of integration

Q: Q4A) Find area bounded by y = 0, y = √2x-x² using double integration.

A: The required graph is shown.

Q: (b) Integrate the following using integration by parts: [5t* Int dt

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Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: We have to find area bounded by the given curve.

Q: 2 (F(x) + x³)dx = ? %3D -1

A: Given that the area under f(x) in [-1,2] is 10br2 So,

Q: Evaluate the integral. (Use C for the constant of integration.) -2t te dt

A: Let the given function is:

Q: Find the c that satisfies the MVT for Integrals. f(x) = x² [0,4]. over

A: Given: f(x)=x2,  [0,4]

Q: Find the area between the curve y = 4 and the line y =-x+3, as shown in the x+2 region below. b, Use…

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Q: 1. Find the area of the shaded region by (a) integrating with respect to x and (b) integrating with…

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Q: Find by double integration the area bounded by the given curve, y2 = 4x & y = 2x - 4

A: If a region is bounded by the curves f(y) and g(y) over the interval [a,b], then the area by using…

Q: How many times do you need to integrate by parts to reduce ff(In x)° dx to an integral of In x? ·

A: Given integral is ∫1eln x6dx

Q: Evaluate the integral. (Use C for the constant of integration.) X + 17 J dx x² + 16x + 68

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Q: 64. y cos(x³ – 1) dx dy y/2

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Q: Evaluate the integral. (Use C for the constant of integration.) 10 dx 5x + x/x

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Q: Evaluate the integral. ( Use C for the constant of integration. )

A: The given integral is ∫x+21x2+20x+104dx. Evaluate as follows.

Q: For the area bounded by the x-axis and the function f(x) = x² – 3x + 2, using Euler's Forward…

A: Note: We are not given number of steps for the approximation. Graphical Representation:

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

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Q: Evaluate the integral using tabular integration by parts. |(4 2 – x + 2) e* de +C

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Q: Evaluate the integral -5earctan(y) - dy 1+ y?

A: We have to evaluate the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) | VER-X² dx 81 x

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Q: Evaluate the integral. (Use C for the constant of integration.) x dx

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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.