(x can be transformed into Jf(z)dz, Determine the value of Using the substitution X=7, the integral expression f(z) for z=3.65.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

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Q: Evaluate the integral. (e* i + 4t j + In(4t) k ) dt + C

A: The given integral is: ∫et i+4t3 j+ln(4t) k dt

Q: Substitute u = x + 2 into ul0 - 2u° + C to evaluate the given integral in terms of x. 10 | x(x + 2)8…

A:

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: Evaluate by algebra dx 1. S 3 1+ √x+1

A:

Q: Use Romberg integration to compute R3,3 for the following integral x sin x dx

A: Given integral is, ∫01xsinx dx Then, h1=b-a=1-0=1h2=b-a2=12h3=b-a4=14

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: 8x Evaluate the given integral Jo (4+x²)2 dx using the substitution u = 4 + x². A. Estimate to three…

A: topic - definite integration

Q: Evaluate the integral of (t2) / √(1+t2 )with respect to t.

A: It is given that, f(t)=t21+t2 It is known that, ∫1(x2+a2)dx=logx+x2+a2+c and…

Q: For f x 1/2 dx and using the substitution=x1/2, the resulting integral takes the form: -du 411…

A: We know that integration of xn is nxn-1.   Here i attached the solution of this question.

Q: To evaluate the integral f(x)dx, the substitution u= g(x) is used. Thus if g(x)= e* then dx =

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Q: Next, integrate with respect to 0. T/2 1 e4 1 - de = 1. | T/2 1 - e4 Again, apply the Fundamental…

A: Here, all the parts are correct except part 3 of 6. The part 3 of 6 is: Evaluate: 12∫0π21-1e4dθ

Q: 3. Evaluate the given integral. d.x V1 – x

A: The given integral is ∫-1011-xdx. Let u=1-x. Then, du=-dx. The upper limit becomes u=1-0=1 and the…

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: Use the substitution technique to determine the following integrals:

A: Important integrals for the question: ∫sec2 x dx = tan x + c ∫un du = un+1/(n+1) + c Other important…

Q: A. Evaluate the following integrals by substitution. 1. fx(2x2 + 3)%dx x5 2. S; dx (x6-8)2 3. Sx V1-…

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Q: S(e-3y V6 + e- 3y 2y3+y -)dy y4+y2+1 -

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Q: The particular integral of (D² – 2D+ 1)y = xe® is 2 -2et - x2 3

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Q: 2. Evaluate the following integrals a)S3z dx 314r b) S dt

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Q: C * dt = 1 0.2t

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A: We need to evaluate the integral using the given substitution

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A:

Q: The particular integral of (D² +1)y = x is

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Q: Evaluate the integral. (Use C for the constant of integration.) dt t4 + 10

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Q: 2. Evaluate the following integrals. (a) J sin° (2) dæ 3x2 + 2x + 7 (b) dx x² + 1

A: We have to solve the given integral.

Q: -dr evaluate the integrals by substitution method J 2dx V2+r /2+x

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Q: Derive a reduction formula for the integral of (e^mx)/e^n , where m and n are constants

A: solution of the given problem is..

Q: In evaluating | x(4 – x)3dx , if we use the substitution that u = 4 – x, then what will be the…

A: Indefinite Integration using substitution

Q: Given: (25(x)dx e-x3 There is a function f (x) such that when u = -x³, the resulting integral is…

A: topic - functions

Q: Given: ((x)dx Evaluate f(v2). There is a function f(x) such that when u = -x³, the resulting…

A:

Q: Derive a reduction formula for the integral of (e^mx)/x^n , where m and n are constants

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Q: I = x²Vb – xdx a

A:

Q: e2z Q5- The value of the integral . Where C is Z = |3 (Z+1)*

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Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: S(e-³y V5 + e-3y 2y³+y -)dy зу - y4+y2+1

A: Given,

Q: G(x) = ∫^1vx xt2 dt (1 is the number on top of the integral sign, x on the bottom)

A: Given integral is:Solving the indefinite integral: The antiderivative of a function of the form xn…

Q: Find the forced solution yF (x) at xo Cr³ + c2x³ In(x). 2 to the following ODE in terms of a…

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Q: Evaluate the integral. (Use C for the constant of integration.) t2 dt 1 - t6

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Q: Substitute u = x + 2 into u10 - zu° +c to evaluate the given integral in terms of x. 10 x(x + 2)8 dx…

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Q: i +j- t3/2 k ) dt |

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Q: Find the following integrals using the method of substitution. t2 dt /6+t3 x2 b) J ; dx 5x3+8

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

Q: Find the integral of t/(t^4+2) dt

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Q: Evaluate the following Integral by using suitable method S(e-4YV1+ e-4y 2y3+y dy y4+y2+1/

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Q: 81. The particular integral of x2 d²y A) 3x +y = is |3D de 6x 769

A: We can find the first and second derivative for the given options and check in the  differential…

Q: The integral reduces to Sk, where u = f(x) and for some constant k . Compute f(1). e*+1 e+1 A B e-1…

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Q: Let F(x) be an antiderivative of f(x). If F(1)=12 and the definite integral from 1 to 4 of f(x)dx =…

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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: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A: To find: The integral ∫dt1-7t6. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C

Q: Given: (25(x)dx e-x3 There is a function f (x) such that when u = -x³, the resulting integral is f…

A: Let's find.

Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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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.