7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

Q: Evaluate using integration by parts. .6 In (x)dx 6 In (x)dx =| 1 (Type an exact answer.)

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Q: 4 sin 3y–6 dy cos 3y

A: We'll evaluate the integral as following.

Q: ! 6-Find the value of the integral * U x3/2 e-x dx

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Q: 2. Compute the indefinite integral xe dx

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Q: 7. Evaluate the integral. J CoS X dx 0 1+sin2x

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Q: S 6x®cos (x³) dx „8, ,3•

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Q: 3. Evaluate the integral Sx cosx dx.

A: Please see the below picture for detailed solution.

Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: B) Use the techniques of integration to evaluate. (Solve 2 only) 3) J tan-ty dy dx 2) (1– x²)5

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Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: Q3. Use tabular integration by parts to evaluate the following Integral (x² +x+ 1) sin x dx

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Q: dr

A: Given integration is : ∫x2-9x3dx To find the value of integration.

Q: 2.Find the following indefinite integral without substitution. S sec y (tan y- sec y)dy

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Q: 3. Find the indefinite integral: Sx(x-2)* dx

A: Please rate

Q: 3. Evaluate the indefinite integral 1 -dx x' + 3x? 3

A: Given,

Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

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

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

Q: ex What is the integrable form of dx? e* - e -X

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Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: 5. Evaluate the integral: Jsin?x cos'x dx

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Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: !!! 6 cos (x2) Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Triple integral

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. Integrate f over the given interval of x, using…

A: Consider the provided question, fx=sin2x+cos4x, 0≤x≤1. We need to Integrate 'f' over the given…

Q: 2) Evaluate the integral. T/2 L cot³x dx

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Q: Q1:Choose theappropriate value to integrate the following sin(In x) dx (sin (In x) – scos (In x)) +…

A: Solution I=∫sinin x dx        Let  lnx=t⇒x=et         1x dx=dt          dx=xdt…

Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: TX Evaluate the integral dx dy by reversing the order of integration. 2 Cos 0.

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Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

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

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Q: 5. Evaluate the integral. (Use C for the constant of integration.) sin³ (y)cos (y)dy

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Q: 7. Use integration by parts to prove that for any positive integer n, п - 1 Scos | cos"x dx = 1…

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Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: 5) Evaluate ehe integral (use c fos Ane constant of integration. tan'cx)cos x) dx

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Q: 15 Find the integral | 2/x (1+x) dx.

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Q: 57 Evaluate the integral |[xy dy dx. 12

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Q: 3+n (2x) dx By specifying the +ype of examine it by explainings conveyere integral, x --

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Q: 9/u The evaluation of the Integral of S° sin2x cos4x dx is

A: we have to integrate

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: a) [ ]: Evaluate the integral (4x + 1) In x dx c) [ ]: Evaluate the integral 2 dx (x – 1)(x + 4) |

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Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

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Q: Q4) Evaluate the integral 0.5 0 N=6. x sin(x) . dx using trapezoidal rule taking

A: We need to find the value of integral ∫00.5xsin(x) dx using trapezoidal rule. f(x)=xsin(x) then step…

Q: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

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Q: 3. Find the indefinite integral. S (3e* + +x³ + 3) dx

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Q: 13. Evaluate the integral dx x – 1

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Q: 15. Evaluate the integral 10 ·dx (x – 1)(x² + 9)

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Q: Q.4 Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx

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Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration