70 (sinr cos r) dx T/2 sin a) dx

Q: Use an appropriate substitution to show that the value of the following definite integral has value…

A: SOLUTION-

Q: Consider the following integrals 4 sin? x -dx x2 + 6 00 e9t dt i. e9t – 1" Mark the correct one for…

A: Step:-1 Since, we know cos2x = 1- 2 sin2x⇒2 sin2x = 1 - cos2x An integral is called convergent if…

Q: Find the following indefinite integral. Use C for the constant of integration. VI + 3 V) dx Answer

A:

Q: Use integration by parts to evaluate the following Integral S3 cos x? dx

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Q: Solve the following integral using the integration by parts method. (i) |x² sin mx dx (ii) e* cos 3x…

A: We can find the integration using by parts method

Q: b. I = S(1+ sin x)5 cos x dx

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Q: (x² + 2x) cos(2x) dx

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Q: 5πT sin' cos dx 4х 8.

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Q: Approximate the following integrals using the Trapezoidal rule. r0.35 2 dx x2-4 1. 2. Sfx sin(x) dx…

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Q: I = S(1+ sin x)³ cos x dx

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Q: sin(6x) Vi? +4 dt 7

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Q: Approximate the following integrals using the Trapezoidal rule. c0.25 (cos x)? dx b. x In(x+ 1) dx…

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Q: a) Evaluate the following Integration by parts for definite integrals. i) So xe-s*dx ii) 12 Sin-'dx

A: The given integration is  I) ∫01xe-5xdx II) ∫032sin-1xdx

Q: Evaluate the following integrals TC 2x a) -e + sin dx V3x 0. 3. cot(-2x) csc?(-2x) dx b) 7.

A: (a) I=∫0π53x-e+sin-2x3dx =∫0π53x dx-e∫0πdx+∫0πsin-2x3 dx  ∵∫(u+v) dx=∫u dx+∫v dx…

Q: c) Evaluate the following Integration by parts for definite integrals. -5x dx хе 3 ii) . 2 Sin-dx i)…

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

A: To evaluate the integral by making the given substitution

Q: Evaluate the following integrals (from A to E) A. Integration by parts cos dz i) (3t + t?) sin(2t)…

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Q: Evaluate the following by changing the order of integration: 5 sin(y*) dy dx. 5x

A: First we change the order of integration and find limit of integration.

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

A: see below the calculation

Q: Q2 - Evaluate the following integrals i. S cosx sin*x dx

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Q: Evaluate the following integrals S, sin () cos" () dx ) dx

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Q: Evaluate the following integral by changing the order of integration. I | cos(x*) dx dy

A: We have to evaluate the integral by changing of order.…

Q: 4. Calculate the following integrals by using the integration methods. (4x* + 8x3 + 15x)dx (a) dx…

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Q: dx 4-e4x S sin 0 V1 – cos 0 d0

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Q: Integrate the following integrals using either integration by parts or integration by substitution.…

A: The given integral is ∫xsin1+x32dx. Take u=x.  Then, du=12xdx⇒du=12udx⇒dx=2udu Note that,…

Q: dx 16. 2 2 x*Vx –16

A:

Q: Approximate the following integrals using the Trapezoidal rule. -0.35 2 -dx x2-4 1. 2. Só x sin(x)…

A: 1.The given integral is, ∫00.352x2-4dx Here, f(x)=2x2-4,taking h=0.05 Let us construct the table as,

Q: |/ (cos(x) + sin(x))² dx

A: *Used the (a+b)2= a2 + 2ab + b2 formula.

Q: Approximate the following integrals using Gaussian quadrature with n = 3 and compare your answers to…

A: The Gaussian quadrature 3-point formula is  ∫abf(x)dx≈b-a259f(x1)+89f(x2)+59f(x3) Where,…

Q: First make a substitution and then use integration byparts to evaluate the integral.   ∫Cos √x dx

A: Given: I=∫cosxdx for evaluating given integral, we substitute x=t…

Q: Evaluate the integral. (Use C for the constant of integration.) 7 cos (a) da sin(æ)

A: Explanation of the answer is as follows

Q: Perform the following integration. 1. (sinhæ)(coth? a+csch® a) dự sec³ x tan x 2. S dx √2 + sec x 3.…

A: Given: ∫x-1x2+5x+8dx To find evaluate the given integral for the integration if a given function…

Q: By using a trigonometric substitution x = 3sece ,where 0 s0 < 27 "he integral 3 Vx² - 9 dx can be…

A: We have to choose the correct answer from the given option according to the given condition

Q: Given dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given: ∫19x2+4dx Let I= ∫19x2+4dx To solve this we need to the trigonometric substitution

Q: Evaluate the integral. (Use C for the constant of integration.) e cos(50) de

A:

Q: Evaluate the following integrals using Integration of Hyperbolic Functions. 14. S sech? ( Inx) dx…

A: Integration is the inverse of differentiation and we are going to use that concept here. Therefore…

Q: 16. | (ez/a – e-xla)dx. n/3 sec 0 tan 0 do. Vesec e 17.

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Q: Apply the method of substitution to integrate the following integrals: dx I = ; a. Va²-x² b. I = [(1…

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Q: Evaluate the following by changing the order of integration: •3 sin(y?) dy dx. (6 marks)

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Q: Solve the following integrals: i. S(e**sin(2x))dx using integration by parts or tabular meth

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Q: Evaluate the integral. (Use C for the constant of integration.) cos 30 de

A:

Q: Evaluate the following integral. (Use C for the constant of integration.) л tan 8x 2 л dx 2 sec 8x

A: Assume u=8x - pi/2.From there find dx

Q: Evaluate the following integrals using the required method of integration. • Show complete, clear,…

A:

Q: 1. Evaluate the following integral by changing the order of integration. I| Cos(2*) dx dy

A: Topic: integration

Q: Evaluate the integral. (Use C for the constant of integration.) | 9t sin?(t) dt

A:

Q: Consider the following integral: sinx dxdy By reversing the order of integration, the value ofI is…

A: In the question, the limit of x is a function of y. We will change this order and put y within a…

Q: By reversing the order of integration, evaluate the following integral. To ²² x cos (y²) dy dx. co

A: The given problem is to evaluate the given double integral by reversing the order of integration.

Q: Evaluate the integral. (Use C for the constant of integration.) cos (@). 4 da V sin(a)

A: Here we evaluate the integral∫4 cos5(α)sin(α)dα

Q: Evaluate the integrals

A: We have to evaluate the definite integral: ∫-ππ1-cos2 t32dt We know the trigonometric identity, cos2…