Determine the value of the following integral S, tan(x + 4)8(3x – 2) dr where 8(x) is the Dirac delta function.

Q: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: Find the integral of (e^x - 1)/(e^x + 1) dx.

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Q: (b) dx (1+ x²)² 0,

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Q: 14e" dx 1+ e20

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Q: Q2: Evaluate four of the following integrals: 2. 3. 2 log2(x+2) dx (x+2) dx 1. r? cosh(lnt) dt…

A: Explanation of the answer is as follows

Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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

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

Q: The following Delta function integral L; (x² + 2x + 1) 8 (2x – 1) dæ What is a? ||

A: Definite Integral with derac delata function

Q: Evaluate the following integrals: 1) dz |(log = +3)* 2) f(1-y) dy e 3) f(y-1)3 3*5 92 dy 3 32y 4)…

A: since you have posted multiple questions, so I'll solve first one for you , for rest question's…

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: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: Determine the approximate integration of the following using simple & modified trapezoidal,1/3…

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Q: Determine an integrating factor and solve the followir xdy-ydx-(1-x')dx = o 1.

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Q: Evaluate the definite integral. cln 8 So° f (x) dx, ƒ (xæ) =6e* /(5+e*)

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Q: Q2/ Find the value of the following integrals: 1- |((x+y)dx + (y – x)dy), when cis given by, x = cos…

A: The integrals in the form ∫C(x+y)dx+(y-x)dy involve the integration over a particular curve C. In…

Q: Q16: Compute the following indefinite integral xʻe*dx

A: Please find the solution of questions.

Q: Evaluate the following improper integral. If it diverges, then type DNE. Otherwise, find its exact…

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

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Q: Q3) Evaluate the following integrals: sec(tan-1x). tan³ (tan-1 x) A) y = S dx 1+x2

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Q: evaluate the given integral. L (1 + x)/x dx

A: we have to evaluate the given integral  ∫1+xxdx

Q: Q1 - Find the reduction formula for each of the following integrals iv. In = S sinh"x dx

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Q: Q2 Find the integral for the following : dx 1 1-5 2- fe-*sec? (ne-*)dx 3- S dx 2vx+2x 1+e*

A: We have to find the Integral for given expressions. 1. ∫dx/(2√x + 2x)  2. ∫e-x sec2(πe-x)dx  3.…

Q: 1. Find the following integrals using the graph below: g(r) 4 g(x) dx

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Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

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Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 eCos-1x 5. S V1-x2 6. Se…

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Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx =…

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

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Q: Consider the following pdf: fr (X) = 0.06x+0.05 0 <x < 5 Since it is a continuous pdf, calculations…

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Q: Find the indefinite integral.

A: ∫ exex+12dxSubstitute u =ex+1=∫ u2duApply the Power Rule:  ∫xadx=xa+1a+1,    a≠-1=u2+12+1Substitute…

Q: Find values of p for which integral diverges. dx x(In x)"

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

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Q: For what value of a, b > 0 is the following integral convergent. dx . x°(1+x³)

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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: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: Evaluate the following integral using the Beta function: 1 T³ – 3x° + 3x7 – x°dx ,5 8

A: Beta functions are a special type of function, and it is also classified as the first kind of…

Q: Q3/A) Evaluate the integrals S sin(ln x)dx

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Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: Evaluate the following by changing the order of integration: 4 4 cos(y²) dy dx. 2.

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Q: Consider the following integral. S4 f(x) •4 if -4 < x < 0 f(x) dx where 16 - х2 if 0 < x < 4 Rewrite…

A: Solving by definite integral we have

Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

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: Si (e0.5x +sin2x)dx, use n = 4

A: Solution

Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

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Q: dx S. 2x - 1 e

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

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Q: Compute the definite integral below using the results in S '5 I x² dx

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Q: To evaluate the integral * dx we use the substitution e а. x2 1 O b. 1- x2 O d. x + 1 =t

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

Q: Q3: Find the integral for the following functions: - dx 1)) T2-2x+1 Vx2-2x+1

A: we want to find the integral for given function

Q: Find the integral for the following functions: - dx 1) . Vx²-2x+1 2) ſ e3se c(x), sec(x). tan(x) dx…

A: Solution: The objective is to find the value of given integral

Q: Find the indefinite integral. (Use c for the constant of integration. |(ei + 3tj + 16t°k) dt

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.