Find the area between y = 1.2x + 2 and y = x² – 4. Round your limits of integration and answer to 2 decimal places. -5 -2

Q: Use the basic integration rules to find or evaluate the integral.

A: Indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that F'(x)=f(x).…

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: Evaluate the integral. (Use C for the constant of integration.) 8 dx x + 8 +

A: We first rationalize the…

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

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Q: Q1. Sketch the region of integration and write an equivalent double of integration reversed. 14-2x…

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Q: Use the appropriate technique of integration to compute the following antiderivative 1. (x° ln x dx

A: Given that: ∫x9lnxdx

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: 24/ Answer two from the following :- 2-x - Evaluate and change the order of integration in 1 = ²*xy…

A: We have to solve the given problem.

Q: Find the area between y=2x+3y=2x+3 and y=x2−1y=x2-1. Round your limits of integration and answer to…

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Q: aluate the integral by making the given substitution. (Use C for the constant of integration.…

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Q: Evaluate the integral. (Use C for the constant of integration.) [5√16. 5√ 16 + ex dx

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Q: Find the indefinite integral. (Use C for the constant of integration.) 8. dz | zV 49z2 – 25

A: We have to find the indefinite integral.…

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: Find the indefinite integral. (Use C for the constant of integration.) 6 cosh(Vx) xp

A: The given integral is∫6coshxxdxwe will solve the above integral using substitution method.

Q: Evaluate the integral. (Use C for the constant of integration.) 1000e0.1x dx

A: Integration

Q: Q3] Use the trapezoidal rule of integration to determine the value of S, xlnx dx with h = 0.1, work…

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Q: Find the area between y=1.2x+2y=1.2x+2 and y=x2−4y=x2-4. Round your limits of integration and answer…

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Q: Find the area between y = 5 and y = (x – 1) +1 with x > 0. If needed, round your limits of…

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Q: If f(x)dr what are the bounds of integration for the first integral? a = and b

A: If ∫abf(x)dx=∫-65f(x)dx+∫58f(x)dx-∫-6-2f(t)dt To determine the bounds a and b.

Q: Write the general antiderivative. (Use C for the constant of integration. Remember to use abs 1 3x…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 5 cosh(Vx) xp

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

A: The required graph is shown.

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: Evaluate the integral. (Use C for the constant of integration.) e2x dx

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Q: Evaluate the area of the shaded region shown below using dxd order of Integration. yA y = 1+x? 2 -X=…

A: Area of the shaded region is given as, Total Area=A1+A2+A3+A4 where Ai, i=1,2,3,4 is the area of…

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: To find the integration.

Q: Evaluate the integral. (Use C for the constant of integration.) | 2000e0.1x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx Vx + xVx

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Q: Find the area between y = 1.5x + 4 and y = decimal places. – 3. Round your limits of integration and…

A: the given curves are: y=1.5x+4y=x2-3 we have to find the area between the given curves. we have to…

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t°i + 12tj – 2Vtk) dt

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Q: Express the integral in terms of the variable u, but do not evaluate it 2 Зжу 25 — х? dx; и — 25 —…

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

A: Solve for the area

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: xcos(4x)dx

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: evaluate using Integration by Parts.

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Q: Ql Find the Valite of integral

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

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

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Q: C dady y!/3 Reverse the order of integration and evaluate the integral.

A: On Change the order of integration will  not effect the solution. By changing the order of…

Q: Q4- BY usin simpson rule for integration find J=Jo' e* dx. n=10

A: J=∫01e3xdx.   N=10 f(x)=e3x h=b-aN h=1-010=0.1 The value of table for x and y x 0 0.1 0.2 0.3 0.4…

Q: Q1) Using numerical integration to estimate the area (r=4 )and c(4,0) with n=4 of the semicircle

A: Trapezoidal rule: One of the most significant integration rules in Calculus is the "Trapezoidal…

Q: Use integration by parts to evaluate the integral. Round your answer to the nearest tenth. In(z) S²…

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

A: Given query is to setup integral for area inclosed by given curves.

Q: Q4. a) sketch the region of integration, reverse the order of integration, and evaluate the…

A: The given integral is ∫02∫04-x2xe2y4-ydydx. The objective is to integrate the given function by…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) y²(5 – y³)2/3 dy

A: Let I = ∫y2(5 - y3)2/3 dy   I = ?

Q: Find the indefinite integral. (Use C for the constant of integration.) 3t V9t4

A: Here, we use the formula shown on  board.

Q: find the indefinity integral  x^9 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) x^2/(49 − x^2)^1/2 dx

A: I =  ∫x249-x2 dx   I = ? Formulas: 1. ∫dxa2 - x2 = sin-1xa + c 2. ∫a2 - x2 dx = xa2 - x22 +…

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.