Observe that f is a linear function; what kind of function is A? Using the formula for 4(x) that does not involve integrals you found on the previous slide, compute A'(x).

Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: he resulting integral of dx is ax + b ln x -Arctan +C, where a, b, d, e, and x3-2x2+5x are integers.…

A: b=2

Q: compute the value of f f(x) dx? If so, what rules would you use to calculate the value of this…

A:

Q: According to numerical methods, the integral of a function f(x) over the limits a and b can be…

A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: 2. Compute the following. When evaluating the definite integral, change the limits of integration.…

A: (a).  The given integral is: ∫x21+x35dx

Q: In the function given. Evaluate the integrals.

A:

Q: 2. Use a substitution to change the integral into one found in the table of integrals, then…

A:

Q: If you are asked to find the indefinite integral of f(x) = x ln(x), and you are told to integrate by…

A:

Q: Obtain a formula that expresses the integral ∫cosn x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) Зx In(x) dx ,2 -36

A:

Q: Use the specified substitution to find or evaluate the Integral. (Use C for the constant of…

A: The given integral is ∫x-5x+8dx. The main objective is to evaluate the integral by the substitution…

Q: (2+ v 9-x²) dx -3

A: Given integral is ∫-302+9-x2dx.

Q: Find the indefinite integral. (Use C for the constant of integration.) dt t4 + 1

A:

Q: Evaluate these definite integrals: L, ¢x³ – 3x + 2) dx a. 2e b. S"( cosx – ) dx (Vz – z) dz с.

A:

Q: Suppose a strange particle travels with a velocity (m/sec) of v(t) = , where t is the time it has…

A: velocity v(t)=1t+1 find the travel between t=1 and t=2

Q: P (a, b) = So -at² _e-bt2 dt %3D t2

A:

Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

A:

Q: 1. Sketch the graph of the function y = f(x) = 3 – V4 – x² over [-2, 2] and use this to evaluate the…

A: Given: The function y=f(x)=3-4-x2,             Interval: [-2,2]             Integral:…

Q: Evaluate the integral of sin^6 x dx from 0 to T/2.

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Q: Find the integral of f(x) = e- sinh(x) between 0 and 1.

A:

Q: evaluate the given integral.

A: we have to evaluate the given integral: ∫x2+5x-1x+4dx let the given integral be I. therefore,…

Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: A function f(x) contains the following points: (1.00, 0.90), (2.00, 3.00), (3.00, -4.50), (4.00,…

A: Given information: A function f(x) contains the following points: (1.00, 0.90), (2.00, 3.00), (3.00,…

Q: Use reduction formula to evaluate the given integral xe" dx

A:

Q: Find formulas for the functions represented by the integrals.

A: Find formula for the function represented by the given integral: ∫1x2 t dt

Q: In(x) Differentiate the function F(x) = | cos(e e') dt (for x>0)- 1/x Show and justify your work.…

A: The given function is: Fx=∫1xlnxcosetdt To differentiate the given function.

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: Provide an appropriate response. Given f(x) dx = 4 and g(x) dx = 2, use properties of definite…

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Q: In the function given. Evaluate the integrals.

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Q: Use Taylor's formula with a = 0 and n = 3 to find the standard cubic approximation of f(x) = y at x…

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Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

Q: The value of the definite integral fm12 √ex - 9 dx is in the form F(b) – F(a), where a In 9 and b…

A: We have to solve given Questions.

Q: consider the function y (x) = ln (x), from (1,0) to (3, ln (3)) b) Set up the integral that…

A: Setting up the integral

Q: Evaluate the integral. (Use C for the constant of integration.) p3 In(p) dp

A:

Q: Given the function, f (x) = 99x4 + 99x3 – 2x2 + 9x + 0.2 Estimate the value of the integral bounded…

A:

Q: Evaluate the integral of (e^x)^(1/2)

A: Given the integrand (e^x)^(1/2) Evaluate the given integral using u-substitution method. Let

Q: For p > 0 and a > 0 express the following integral in terms of the gamma function: tP-le-at dt.

A:

Q: the integral , dx is equal to: -2 x2+4x+5 4 2 the above the above

A: We will find the solution of the integral.

Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

A:

Q: 1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the integral. (Use C for the constant of integration.) R - 9x In(x) dx x² – 25

A:

Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: Use the special or Bessel function to solve TWO from the following integrals In x 1. [ dx x* +1 2.…

A: It is given that

Q: Evaluate the integral. (Use C for the constant of integration.) 16 In xp (x^ +C

A: Topic:- integration

Q: 1. Given that | f(x)dx=4, which of the following integrals can be computed using a substitution? If…

A: To evaluate  the given integrals.

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: (x 2

A:

Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

A:

Q: Only one of these calculations is correct to evaluate the definite integral Vx+1 dx Using the…

A:

Q: For what values of  a is ∫0∞ eax cos x dx convergent? Evaluatethe integral for those values of a?

A: ∫0∞eaxcosx dx Now, ∫0∞eaxcosx dx=limt→∞∫0teaxcosx dx=limt→∞eaxa2+1acosx+sinx0t    ∵∫eaxcosbx…

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A: See attached file for a step by step explanation to find the required Integral.

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.