8 dx 2) Evaluate the integral Is x/x² – 16 Hint: Use a suitable u-substitution. You may find the following formula from differential calculus useful: tan-() = d a dx x²+a?

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: 4. Yes, more integrals to solve! 1 dx x/lnx tan x dx COS I b) / e* dx a)

A: 4. It is asked to evaluate the given integral .

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

A:

Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

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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: 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: 3 2x To find the definite integral dx, apply the basic integration rule. Vx? + 16 Let u x + 16.…

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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: J, 3x +1 dx 3. Find the exact value of the given definite integral *, 6 dx 4. Evaluate the given…

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

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Q: dx Given that /2 || 1+sin² x 2/2' ) please evaluate the double integral CT/2 pT/2 1 dx dy (1+ sin?…

A: We have to find value of given Integral.

Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

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Q: 0.4 a) Approximate the integral dx using Simpson's Rule with four (4) subintervals. Give the answer…

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Q: 4 dx Vx(1 + x) roper for two reasons: The interval [0, co) is infinite and the integrand h 4 4 dx =…

A: Here we use substitution so simplify the integration.

Q: 13. If u(x) = sin 3x and v(x) = x, what are du and dv? Writedown  u dv and  v du in this…

A: Given- ux=sin3x and vx=x To Find- The value of du and dv, write down the value of ∫udv and ∫vdu,…

Q: 3. (a) Evaluate the following integrals: (1) / 2x + 5 dx x – 3 (ii) / sin(tan 0) de cos? 0 = [ dt…

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Q: Q2 Find the integral for the following : dx 1 1-5 2- fe-*sec? (ne-*)dx 3- S dx 2vx+2x 1+e*

A: We have to find the Integral for given expressions. 1. ∫dx/(2√x + 2x)  2. ∫e-x sec2(πe-x)dx  3.…

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

A: Explained below

Q: 0.6 3 by taking h = 0.1 fx-e* - dx solution of the integral with Simpson's which one? · method 8

A: Here we have find find integral of given function using simpson's 3/8 rule

Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: Given integral is

Q: II. Evaluate the following integrals: 7 ax 52X+7 13. [ sin x 2 - cosX (1x dx 14. S MA sec² 3x -dx 1…

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Q: 79. What are the new limits of integration if we apply the substitution u = 3x +7 to the integral…

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Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd .

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: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: 12 »4 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact…

A: Given:    Double Intergral is given

Q: Show that u (X ) = 3X+ 2x is asolution to the integral equation 3(1+x)? X - S sinh (x-t) ultJ dt

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Q: Sin (x-t) u(t) dt = 1- Cos x

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Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: Q3/A) Evaluate the integrals S sin(ln x)dx

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Q: dz

A: Here I am attaching image so that you understand each and every step.

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

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Q: 1 2. Evaluate the integral using integration by parts. Hints: LIATE, 은(cos-1(x)) : dx 1-x² cos-(x)…

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Q: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

Q: Evaluate the integrals: 1- dx TT/2 7cos t sin t dt 0. 2-

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Q: Q4: Find the value of integral 1 1 1. 1+x4 1 V1–x²dx 1 cos(x + 1) dx 2. 3.

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Q: Q2:A/ Evaluate the integrals 1/x sec (1 + e) tan (1 + e) dx Q2:B/ Find dy/dx Vidt sin x cos t dt 2

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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: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: o integrals are equivalent and (b) calculate 2. | sin(t) dt = sin(x + 1) dx %3!

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

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Q: 22.9 Use numerical integration to evaluate the following: d.r Ca) (b) e- sin? y dy x(x +2)

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

Q: The definite integral from 0 to = of cos x sin xesin² x dx is 4 O e - 1 e+1 e-1

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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