4) Solve the following integral by rectangular and trapezoidal methods integration (xsin (x) cos (x) dx: (0 < x < pi / 2)

Q: Evaluate the integral. Зп /4 6 sin (x) cos (x) dx Jn/2

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Q: Q4) Solve the integral by Simpson's rule x3 cos2x dx, h 0.2

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Q: a) b.) O F+ x dx (x³ +1) ³ 3 Sinx sin 2x dx 2 cos x

A: 1. The given integral is ∫01x dxx2+13. W have to evaluate the given integral.

Q: 3. Find the following definite integrals. (2x +3)dx (x2- 1)dx x² - 2x)dx sin(3x + 4) dx 1

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Q: 2. Find the following indefinite integrals. Use Substitution and/or Integration by Parts when needed…

A: a) Evaluate  ∫sinθcos4θdθ         ...(1) Simplification: Put cosθ=t⇒-sinθdθ=dt in (1)…

Q: 3., J(5 cos x+4 sin x) dx

A: We have to find integration

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: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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Q: Find the indefinite integral ∫x cos 2 x2 dx

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Q: '1 1 Given that x² dx = use this fact and the properties of integrals to evaluate (8 — бх2) dx.

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Q: Obtain a formula that expresses the integral ∫cosn x dx

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Q: 4 sin x dx (1+ cos x)2

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Q: Evaluate the following indefinite integral. Use C for constant of integration. * cos(10x) + sin(20x)…

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Q: 4) Evaluate the definite integral: S, (2x² – 4x + 6)dx. -

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Q: Find the indefinite integral. X COS 10nx2 dx

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Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: 37. Use numerical integration to estimate the value of c0.6 sin- 0.6 = dx Vī For reference, sin¬ 0.6…

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Q: Which of the following integrals is NOT appropriate for a substitution method? A 5x*sin(x³)dx ®…

A:

Q: Solve the following integral by drawing the bounds of integration, reversing the order of…

A: The limit of the integration is  y = (1/2) x  to y = 2 And x = 0  to x =4 Now order will be revereto…

Q: 4. Evaluate the following integral by trigonometric substitution [Apply the method that was taught…

A:

Q: 4. The following integration can be solved by using the Substitution technique, where we have 수 U =…

A:

Q: Q1: Evaluate the following integrals by using a substitution to reduce it to sec X dx 1 standard…

A: We have to use substitution method.

Q: Evaluate the integral.  integral  cos 2 x sin 2x  dx

A: Given integral to evaluate  ∫cos2xsin2xdx substitute sin2x=2sinxcosx ∫cos2xsin2xdx=∫cos2x2sinxcosxdx…

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

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Q: 2. / 3" csc²(3") sin“(3") da (3") sin®(3") dx

A:

Q: 2. Evaluate the integral: (a) ſe -3x sin 5x dx

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Q1: Evaluate the following Integration: a) ( In(x²+x)-Inx-en3 dx b) S; sinx Ine(x+1) 1-cos²x

A: Answer (a): To evaluate this integral, apply the logarithmic properties : And, And, And, And,…

Q: 1. Find the general indefinite integral. 5e + 3 sin x dx (b) ["be²

A: We have to solve this given integral . For this first we solve the general indefinite integral &amp;…

Q: 10 Consider the definite integral cos(1 + √√x) dx A) To estimate this integral accurate to four…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Use the value of the first integral I to evaluate the two given integrals.

A: It is given that, I=∫0π/2cosθ-2sinθdθ=-1 Consider the integral ∫0π/22sinθ-cosθdθ

Q: Question 2 Evaluate the following integrals using the appropriate rules of integration. 2.1 S(cos x…

A: (2.1) Given- ∫-π2π2cos x-1 dx To find- Evaluating the above integral using appropiate rules of…

Q: , 1. Take the following integral numerically using an end corrected method. (n-7, h=0.001) (give…

A:

Q: Evaluate the following integral.

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Q: 2. Using an appropriate method, compute the following integrals. dx x² + 3x + 2 (i) sin³x cos*x dx…

A: (i)

Q: 5. Evaluate the following indefinite integrals. 8. **** Power 2 ...... sin.x dx. b-₁f.co₂x² dx…

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Q: Solve the following integral by using the Tabular Method. (a) x² cos 4x dx (b) sin 3x cos 4x dx 2.

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Q: Find the indefinite integral ∫ dx / (4 + x)3/2 (a) using a table of integrals and (b) using the…

A: a) ∫dx4+x32 Apply u- substitution : u=4+x du=dx plug all this values in given integral and then…

Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

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Q: cos5 0 sin 20 de

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Q: (a) Solve the following integrals. (i) (ii) x' + 3x? – 10 - dx x(x – 3)(x+1) Integrate er* cos (3x)…

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

Q: 3. Find the value(s) of c that satisfies the MVT for Integrals 4 sec x tan xdx

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Q: 2.2 Evaluate following integrals. .sin VT cos E 2.2.1 dx

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

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Q: S. The resulting integral of sin cos-sino d0 has the form | 2 2 -F(0) + C. What should be the value…

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Q: 4) Evalvate the integral E 4 1+x² dx

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Q: 2.x dx +1, x'

A: Let I is the value of given Integral.

Q: -4 I cosx (0.25x² + 1.90)dx,use n =3

A: Given:        ∫14cosx0.25x2+1.90dx , n=3 The formula for the Trapezoidal rule:…

Q: In approximation of 4e* sin(2x) dx by Romberg Integration, R11 = O 2.6842 O 2.9736 O None of these O…

A: Use the following formulae, to estimate the integral ∫abfxdx by the Romberg integration method.…