Find an antiderivative f(x) for x) in 14. Then compute the definite integral fox) dx = f(1) - f(0). 14 -1 (find all )

Q: Еxercise: 1- Use the Composite Trapezoidal rule with the indicated values of n to approximate the…

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Q: Evaluate the iterated integral. 4 (x² - y²) dy dx -4

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Q: 2. Let f and g be integrable functions such that f(x) dx = 6 and g(x) dx = –2. Using the Linearity…

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Q: Compute the given integral. ICOS Idz +C

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Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: 5. Evaluate the definite integral (1+Inx) а. b. S dx. 2x+3

A: a) ∫1e1+ln x2xdxb) ∫-1112x+3dx

Q: Let H(x) integral ,for -2 ≤ x ≤2.Find the value of s such that H(x)= sH(-x).

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Q: (a) Find an antiderivative of x/16 - x*. 1 4 (b) Compute the integral x'V 16– x* dx. |

A: Explanation of the solution is given below...

Q: Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O…

A: The given function,  g(x)=3x2-ex+cosx  .................................(1)

Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: 1. Approximately compute the value of the following integral, as accurately as possible, using the…

A: Note:- Here, you mention function f(x) is creating little bit confusion for me. Is…

Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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Q: 2x Evaluate the improper integral J dx, if it exists. (x2 + 64)2

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Q: what is the integral of e^(-2a|t|) from -w to w?

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Q: Give a formula for an antiderivative F(x) of f(x) = In(x)(tan¬1 vx) such that F(3) = 0. 1)

A: This is a problem related to differentiation of the function. Based on the product rule we will…

Q: Evaluate the iterated integral. 74 (x² - 2y²) dx dy

A: Given that a double integral we solve this integration by using general property of integration.…

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: Evaluate the iterated integral. 21 4 (x2 – 2y2) dx dy

A: We need to evaluate the following iterated integral ∫12∫04x2-2y2dxdy

Q: Evaluate the iterated integral. T/4 1 Tv cos(x) dy đx

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Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: In(x) Differentiate the function F(æ) | cos(e') dt (for x>0). %3D 1/r Show and justify your work.…

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Q: 3. Evaluate the iterates integral: SL(x-y) dy dx

A: We have to solve

Q: Find the integral. J 3 x√9 - (In x)² + C dx

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Q: Evaluate the iterated integral. 8 3 (x + y²) dx dy -1/1

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Q: +00 dx II. Evaluate the improper integral x(In x)²

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Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: 6 In x Evaluate the iterated integral given that the evaluation of the inner integral is 7x 3 In x…

A: ∫1e∫1e23lnx7xydydx

Q: 14. Find the equivalent integral of * S x(x+1) O-f3dx + f 3d x+1 dx OS÷-1# R x+1 01 Of //dx -…

A: Here we have to apply partial fraction.

Q: 2. a) Compute the integral fa f(x) dx using 5 point composite rectangle, trapezoid and Simpson rules…

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Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

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Q: Use the specified substitution to find or evaluate the integral.

A: Consider the provided integral, ∫01 dx23-xx+1 Evaluate the provided integral. ∫01…

Q: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

Q: 1 d.r. x² In(x) Consider the inmproper integral r10

A: The solution is in step 2

Q: Determine the indefinite integral. S()dx O x+c O 2/x +c O 3 3/x³ + c 2x² + c

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Q: Q2/ Find the integral of, 1/n f(x) * cos(3x) dx , for f(x) =1 on [-n, 0] and f(x) on [ 0, a] (using…

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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: Evaluate the integral

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Q: Q3. Find integral of ( by using Rectangular rule): -38 L Sin(x) In(x + 2) dx , n = 7 24

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Q: 9. Let f(x) x In(10) Find the most general antiderivative. F(x)

A: Given data÷ So,we need to find F(x).

Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: Evaluate the iterated integral. (x2 - 8y2) dx dy

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Q: The modified Bessel function I,6x) has the integral representation /2 2 1(x) = cosh(x sin 0 )d0. Use…

A: We will use given value of x and mentioned process ( trapizoidal / simpson ) to find value of…

Q: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

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

Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: Let f(x) = x³+1, x<1 1 X+4 5 1.8976 x≥1 Use the composite Simpson's rule to approximate the integral…

A: Introduction: The formula for Simpson's 1/3rd rule is given by,…

Q: Evaluate the iterated integral: - 7 -X = S S e-* dydx е 8

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Q: Consider the definite integral. (18x – 1) e9x²-x dx Let u = 9x? - x. Use the substitution method to…

A: We have to find the integrand after substitution.

Q: Q5: Compute by part the following indefinite integral Sx. In x dx

A: Given  that a integration and we solve it by part. We know that integration of Xn  is -  = Xn+1/n+1.…