et ƒ be an integrable function on [–1,3], with the property that for each x E [-1,3], we have I f(t) dt = e*.

Q: * t/3 Evaluate the integral S'(y cos x – 3) dydx. S x -

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Q: Find Particular integral (P.I) (D² -1)y =18

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Q: Find the formula for the function represented by the integral dt 6t+3 %3D

A: use the substitution method  for finding the integral

Q: Suppose h(z) is ANY continuous function which satisfies the condition 1- means 2) O al 27 O d.…

A: Topic:- application of integration and function

Q: Use the identity f(x) dx = f(x) dx + f(x) dx to compute the integral. %3D -A -A sin(t) dt (Hint:…

A: Explained below

Q: Recall that the gamma function is defined by the integral T(a) = ta-le ta-le-t dt, a > 0, and, r(a…

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Q: The set of all values of p which makes the integral x* dx is divergent is a) (-1, 0) b) (-n,-1) c)…

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Q: Find the formula for the function represented by the integral 1 -dt= 5t+1

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Q: Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x –…

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

Q: Example: Evaluate the following Integral CO -x=V2 ry=2 x³ev° dydx Jy=x²

A: Here we use change of order to solve this

Q: Evaluate the integral. dy e 8y 0.015578 Need Help? Watch It Read It

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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: In (T/e) ( (2- sec?x)eme sec³x sec (зА - х) -dx to be integrable using the formula и" du? ? What…

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Q: If f : [0,2] → R is defined by f(x) = 1 if 0 ≤ x ≤ 1, f(x) = 2 if 1 < x ≤ 2. Show that f is…

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Q: In the example shown above, why do we see the notation "f (x) · f (x)" as part of Step 1? f (x) · f…

A: follow next step in which we have to find notation of f(x) . f(x)

Q: The functions f and g are integrable and J f(x)dx = -2, Į f(x)dx = - 8, and I g(x)dx = 3. Use these…

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Q: 1. Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

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

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Q: If m(E) = 0, show that any function f: E → Ris Lebesgue integrable and Se f = 0.

A: Given, mE=0 So, a measurable function f:E→ℝ is said to be Lebesgue integrable  (or simply inferable)…

Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: Exercises 1. Integrate the following function 5 I = S(4x+5) dx %3D -3 (a) analytically (b) Simpson's…

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Q: Question 8 Show using e, 8 methods that the functions f (x) = 1 and g (x) = sin r %3D 1+ x2 are…

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: express L−1[F(s)G(s)]in terms of a convolution integral.

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Q: Evaluate the integral. J-Txe* dx -7(x +1)e -*+C a. O b. -7(x – 1)e*+C Oc. 7(x +1)e-*+C O d. 7xe-* +C…

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

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Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: 1 Сompute L f dx, where f(x)=|x|.

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Q: The functions f and g are integrable and f(x)dx 2. f(x)dx 4, and g(x)dx= -3. Find the values of the…

A: Given, ∫24fx dx=−2,∫27fx dx=4 and ∫27gx dx=−3Concept used:1. ∫aafx dx=02.  ∫abfx dx=−∫bafx…

Q: Question 13 Evaluate the integral: f (z² + y²) ½ dydz -1/2 O v2 + In(v2 + 1) O In(v2- 1) O v2 -…

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Q: The modified Bessel function I,(x) has the integral representation 2 (7/2 1,(x) = n Jo cosh(x sin 0…

A: We will use simpson 13rd  rule  ∫abf(x)=△x3f(x0+4f(x1)+2f(x2)+.......+2f(xn-2)+4f(xn-1)+f(xn)

Q: Question 6 Estimate the integral 1 dx by Simpson's rule using n = 8. Vx3 + 4 a) 00.9361 b) O1.0212…

A: given integral :

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: Let f be an integrable function on [-1,3], with the property that for each E [-1,3], we have | F(t)…

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Q: Evaluate the integral 1 2-x xy dy dx 0 x2

A: Here we have to evaluate the given integral

Q: (a) Decide if the following function is integrable on [0, 2] and if it is so, then compute the…

A: The function is integrable in 0,2. The value of the function x is given by: x=00≤x&lt;111≤x&lt;2

Q: Evaluate F. dr along each path. (Hint: If F is conservative, the integration may be easier on an…

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Q: If 3 7 f(æ)dæ | f(æ)dæ - f(a)dæ, what are the bounds of integration for the first integral? a = and

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: The integral of the given function ſ cos 3ydy is a. sin 3y +sin³3y + . sin³3y – sin³3y +sin53y + C…

A: Topic :- application of integration

Q: Find the integrating factor to make the following ODE exact У(2ху + е*)ӑx -е*dy %3D0.

A: Let's first check if the given differential equation is exact or not!   For the given differential…

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

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Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: Question 2: Use the Green's theorem to solve $(v² +3x² \dx+2xdy which bounded by x=0,y=0 and 4(x² +…

A: We find the given integral by using Green's theorem.

Q: Question 1 For each improper integral below, show that it diverges or find its value. (a) / Valnz…

A: Solve the improper integrals, a) ∫07x lnxdxb) ∫04lnxxdx

Q: Consider the function. |1, 0<x< f(x) = 0, Sx < 1 Find the half-range cosine expansion of the given…

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Q: dy dx (xy + 1)2 9.

A: Given- ∫01∫01xxy+12dydx To Find- The value of the above integral. Concept Used- As the above…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.