6 Use the definition of the definite integral to evaluate | (x? - 2) dx.

Q: Find the indefinite integral ∫ x /√(x4 − 1)   dx

A: Let

Q: Use the Change of Variables Formula to evaluate the definite integral.

A: Use the Change of Variables Formula to evaluate the definite integral.

Q: Jse the Substitution Method to evaluate the definite integral. * (In x)* dx

A:

Q: Use geometry to evaluate the following integral. 2x if 1sx<3 f(x)dx, where f(x) = 11 - 2x if 3<x<8

A: Given the integral and the function:

Q: Which among the following definite integrals is eq f(x)dx -1 (x)dz ?

A:

Q: 3. f(e* – x)dx

A:

Q: Q\ Use all your background to find the integral of the hyperbolic function: sinh ax -dx cosh bx

A:

Q: Evaluate the definite integral. 1 dx За + 3 0.

A:

Q: use the Change of Variables Formula to evaluate the definite integral.

A:

Q: Evaluate the definite integral. et dx J1 xyln x

A:

Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

Q: Evaluate the definite integral. xe dx Jo

A: using substitution method

Q: Use the substitution rule for definite integrals to evaluate the following definite integral.…

A: Given,

Q: -aluate the definite integral (Show your ork). + sin(x) + 1 )dx

A: Using integration ,

Q: Evaluate the definite integral.

A:

Q: X cos(2x) dx Jo

A: topic - definite integral

Q: 8 x3 dx Vx2 + 36

A:

Q: 3x2 dx is equivalent to +1 Using substitution, the definite integral

A:

Q: 1 Use SUBSTITUTION to evaluate the definite integral to three decimal places. xp- 2x +4

A:

Q: use the Change of Variables Formula to evaluate the definite integral.

A:

Q: Which of the following integrals is equal to the integral/ f(3x- 5) dx? |

A: use integartion formula

Q: Use symmetry to evaluate the following integral. x' dx -3

A: To find: ∫-33x7dx

Q: sinh x dx 1

A: The integral ∫sinh-1x dx can be written as ∫sinh-1x·1 dx. Now use integration by parts to evaluate…

Q: use the Change of Variables Formula to evaluate the definite integral.

A:

Q: Consider the indefinite integral 26 dx: (x7 + 6)"

A:

Q: Which of the following definite integrals has the same value as x(5-x)³ dx?:

A:

Q: 4. Evaluate the definite integral by using substitution. x-1 dx (x+ 2)2/3 -1

A: given the definite integral is∫-16 x-1(x+2)23dx

Q: Evaluate the integral ∫x(x - 1)10 dx

A: the given integral is: ∫xx-110dx let the given integral be I. therefore, I=∫xx-110dx substitute…

Q: use the Change of Variables Formula to evaluate the definite integral.

A: Given integral: Now,

Q: Find the indefinite integral. x' + dx +C.

A: Integrate

Q: Evaluate the definite integral. x² dx

A: "Since, you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the indefinite integral f x5e 2x°dx .

A:

Q: – dx x Inx x²+1

A:

Q: Evaluate the integral. 3 3. f(x) dx where f(x) -3 5.

A:

Q: Q6. The value of indefinite integral dx using appropriate substitution is given by V2-4x²

A:

Q: Evaluate the indefinite integral.

A:

Q: evaluate the definite integral.

A:

Q: ²) S₁₂ x ² √ x²+1 dx St 2)

A: The given integral is; I=∫07xx2+13dx   ....(1) As we know the Power Rule: ∫xndx=xn+1n+1+C

Q: the one i circled is the one i am struggling on. i need help with that problem.

A:

Q: Use the substitution rule for definite integrals to evaluate the following definite integral. 2+7)…

A: The given integral is

Q: Evaluate the indefinite integral. Use C as the constant of integration. dx (x2 + 64)²

A:

Q: Evaluate the definite integral. хVx — 2 dx

A: Use substitutions to integration

Q: Incardx (x)dx 4.

A: yes

Q: Evaluate the definite integral. dx x(1+ In æ)

A: Explained below

Q: "evaluate the definite integral"

A:

Q: Evaluate the definite integral. 1 dx V2-x

A:

Q: Use a change of variables to evaluate the following definite integral. 1 2x dx (x² +3)?

A:

Q: Evaluate the definite integral. 2 dz

A:

Q: Use the definition of the definite integral to evaluate integral (upper=4,lower=0) 5 dx

A: Solution: The objective is to find the integral using the definition of definite integral

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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.