Question 1. Determine the following integrals: | 1.1. / 2r sin(a² + 1) dx 1.2. ze

Q: Question 3 Evaluate the following integrals using either integration by substitution or integration…

A: we have given integral  ∫e-xsin4xdx

Q: QUESTION 2 a) Evaluate the following integrals with respect to x. i) f9x cosech (3x)dx -0.5 xsin¯'x…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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: In this problem, you are asked to carefully read Example 6.4.2 of APEX Calculus. 1 The given…

A: An integral is given by, ∫15+x2dx. The objective is to find the correct substitution which is to be…

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

A: Given integral is not an improper integral.

Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: 3. 'Evaluate the integral. 5 dx х0.2

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Q: Question 17 Which of the following is NOT an improper integral? x-dx A -2 Vx2-1 x/2 sec x dx 01 x13…

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

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Q: Evaluate the following integrals and limits. (sin-! x)° dx

A: It is mentioned to solve only part(a):

Q: QUESTION 4 Solve the following integral by using substitution method. S(6- sin3x)' cos 3x dx.

A:

Q: Evaluate the integral. dx 1

A: givenI=∫13x2dxwe know integral formula∫xndx=xn+1n+1+C

Q: Question 1. Evaluate the following integrals using substitution method: |(x-1)(x²–2x)"dx_ a) sin°…

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Q: 6. Evaluate the integral. S-11 sin x cos(cos x) dx

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Q: | Example 8.20. Evaluate the integral to 3 decimal places. 0.5 x dx using Romberg's method, correct…

A: We need to use romberg's method to solve this problem.

Q: 7(xe* +e*)sin(xe*)–14sin(x)dx

A: Evaluation of the indefinite integral

Q: Problem. 11 : Evaluate the integral by reversing the order of integration. 5 5 2e"/y dy dx = ?

A:

Q: Question 003: Complete the following question involving Substitution Method. Given the integral dx…

A: Given the integral  I = ∫ 5 sin(4x-1) dx By substitution method, Take u = 4x-1 du = 4 dx  dx = du4

Q: Question 8 Which of the following is equal to tanx dx to obtain the correct indef inite integral?…

A:

Q: Question 001: Complete the following problem involving Basic Integration Find the following General…

A: Let  f(x)= xn then basic integration of f(x) is xn+1n+1+c , where c is an integration constant.…

Q: Question 6 Evaluate the following indefinite integrals. If you decide to use a substitution, show…

A:

Q: Step 2 To find the integral x Cos Bx dx by the parts fomula, us sin , as Used in the previous step.…

A: Integration by parts ∫u.vdx=u∫vdx-∫dudx×∫vdxdx To find: ∫xcos8xdx

Q: Question 3. Compute the following integrals. 3.1. S(4x2 – 1)'x dx - 3.2. Sx e5x dx 3.3. S x?cos xdx

A: 31) The given question is =∫(4x4-1)4xdx now first of all simplify the function. (4x4-1)4=(4x2-1)22…

Q: Question 3 In the indefinite Integral in(cosh. x +ex). sinh x +e* (A cosh x + ex sinh x + ex In(cosh…

A: The integration are

Q: Question 6 Evaluate the following indefinite integrals. If you decide to use a substitution, show…

A:

Q: Question Eight:- Evaluate the 20 points following integral sinx d²y 2t2 dt dx2 In x Your answer

A: on using leibnitz rule.

Q: Problem 2. Compute the following integrals using integration by parts. Show your whole set-up not…

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Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: QUESTION 5 dx Compute the integral Jx-2)(x-3)(x+2) by showing all the details of your work. Attach…

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Q: Q1) Find the following integrals } 1) S sinh2x sinhx+1 dx 1

A: To solve the given integral

Q: Question 5. Evaluate the definite integrals. a) 8x dx .5 b) S 2 dy

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Q: Question 6. Evaluate the indefinite integral 1 - dx. J x(x² + 2x + 2)

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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: Suppose we wish to find the integral of x dx/(1+x^4), the first step to solve this is by. Using…

A:

Q: cos x dx

A: The given integral is ∫x2cos xdx We have to integrate the given integral using integration by parts

Q: Question (1) Find the Following Integrals: 1 -+3) dx x? (1) S(x² + (2) S(x²(x³ +3)° dx 2 dx 4 (3)…

A: Since you have asked multiple questions, As per our company guidelines we are supposed to answer…

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

A:

Q: QUESTION 1 Solve the following integrals using any appropriate method of integrations: а) xIn(3x…

A: We have to evaluate the integral ∫xln(3x+1)dx by using any appropriate method of integration.

Q: Question 4. Evaluate the following integral. |(r3 + 4)°3x dx

A: ∫x3+423xdx=∫x32+2x3(4)+423xdx  [expanded the square]=∫x6+8x3+163xdx=∫3x7+24x4+48xdx [distributed the…

Q: QUESTION 12 Evaluate the integral by changing the order of integration in an appropriate way. x sin…

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Q: Question 1 (i) Determine the following integrals (a) |cos? xsin xdx 1 -dx (b) J -5x+6 x² – (c)…

A: We have to find the integrals.

Q: Step 2 1 To find the integral S H x cos 8x dx by the parts formula, use u = x and v = Apply the rule…

A: This is a problem related to integration. Based on the general formula of integral by parts we will…

Q: 16. Find the indefinite integral: Sox - 4) dx

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Q: -cos-sino de has the form sin 2 2 -F(0) +C. What should The resulting integral of 4 be the value of…

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Q: QUESTION 6 Evaluate the integral. Give an exact answer. x?In(2x)dx [Ans] Show your work separately…

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Q: Question 1 Employ integration by parts to compute dx = ax'e- + de + K.

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Q: Question 3: Find the integrali(using u-substitution) Ses (8x+1) dx

A: To evaluate: I=∫cos (8x+1) dx