Subject: EnggMath 4 Integral Calculus Midterm Activity #1 Topic: Integration by Parts Evaluate each of the following integrals. 1. f8tetdt 2. "(1 – 3x) sin x) dx r2n 3. L, w?e+wdw 4. (2 - x)² In(4x) dx 5. S(6+ 3z) cos(1+ 4z)dz 6. Se3-2 sin(2 + z)dz 7. Sxe3*dx x sec x tan x dx 9. fx arcsin x dx 10. S In(x + 1)dx

Q: 1/b [(x2+a}*/>] 5x The resulting integral of J x3+x²+4x+4 dx is In + e Tan-1+ C where a, b, d, and e…

A: The given integral is ∫5xx3+x2+4x+4dx rewrite the integral as…

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Q: Example H-W : 1) Evaluate the following integral : A) iG-)° at , B) žeil dt , c) , elt+0!dt

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Q: 3. One version of the Fundamental Theorem of Calculus tells us that if F is any antiderivative of…

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Q: 1-sin8 Evaluate the iterated integrals r2 cose dr de A 1 B) 2 D) 3

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Q: X-2 dx Evaluate the integral: Sein(x²+3x-7) A x²+5x+In|3x-6|+C B ++ In|3x-6|+C 2 5 © +²2+5x+In/x-21…

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Q: Using integration by parts, the integral ſ x² sin(4 x) dx is equal to: (4x +1) sin x+8xcos.x+C…

A: By using integration by parts formula, we calculate the given integral.

Q: Нomework: a) Evaluate the following integrals 1) | xe3x dx 2) x2 sin x dx 3) | x sin 2x dx

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Q: Review in Integral Calculus 1) Find S x²e*³+1dx. Answer: e**+1 + C Solution: Use Integration by…

A: Topic -- integration

Q: dx Evaluate J x+5 A. Arcsin ( x +2) + C B. Arcsin (x +1) +C C. Arctan (x + 1) + C D. Arctan ( x + 2…

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Q: 1. The study of integrals in calculus is motivated by the problem of calculating A. the slope of a…

A: 1. The study of integrals in calculus,2. antiderivative of f(x)=sinxcosx3. 3x2+2x+C

Q: 42–45. Symmetry in integrals Use symmetry to evaluate the following integrals. /4 r/4 42. tan x dx…

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Q: (2– sec?x) cma/e°sec³x sec( 3A – x) What should be the value of A for dr to be integrable using the…

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Q: h(q(x))q(x)dx = | 7cos(x)eSin(x) dx h(u) du to the integral The most effective way of applying the…

A: If we take u= sinx then du = cosx dx  and h(u)=eu

Q: sin x? dx dy 6 5- 1.5 y 0.5 1 -0.5- -1.5- 11 -1 1 3 6 6- 5- y 0.5 3 1 3 -0.5 -1.5 1- -1 1 3 4. 6 -1-…

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Q: culate and fully simplify |1° cos(z) dz. t: Considering a mnemonic for integration by parts |u dv =…

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Q: Evalua te iterated integral the -1 x+y dx dydz -2

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Q: Activity 2. Using U Integral of the following. 1. S sec?x dx 2. S Substitution or Integration by…

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Q: 23-30. Repeated integration by parts Evaluate the following integrals. 23 fre'a 25. Je sin 4x de 24.…

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Q: Definite integrals Evaluate (i + 3 cos 4t k) dt.

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Q: Tutorial Exercise Evaluate the integral. 8x cos(5x) dx Step 1 To use the integration-by-parts…

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Q: 20) Using integration by parts, if J cos(Inx)dx = uv + J sin(ln x)dx, what is uv? A. cos(In x) B.…

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Q: Question: Integrate the following indefinite integrals. Inx dx a) S b) ſe2* cos3x dx x+4x Inx?

A: a) Given function to integrate ∫lnxx+4xlnx2dx=∫lnxx1+8lnxdx substitute u=lnx,…

Q: 2-7. Basic integration techniques Use the methods introduced in Section 7.1 to evaluate the…

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Q: lmtegral which involved V9+I ou integrate to get 2 sec 0+ cos 0+ C. What is the final answer (in…

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Q: 9-36 Evaluate the integral. So 36 - 9. x'V16 + x?;dx 10. dx V9 6, Vx² 1 dx 13 - dx 36 - х2 11. 12.…

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Q: Question 008: Complete the following question involving Integration by Parts Method. Given the…

A: Let us assume u=18x2du=18(2x)dxdu=36xdxdv=e9xdxv=∫e9xdxv=19e9x

Q: A B C d Using integration by parts, Then k is? (a)-1.5136 5²x² ²x³ cos (x²) dx = k - S²x - [*x…

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Q: 8-11. Integration by parts Use integration by parts to evaluate the following integrals. cIn 2 3t dt…

A: Note: According to the guidelines only three parts will be answered please upload remaining parts…

Q: dx -1/2 V1-x2 Evaluate the following integral with (a) analytically, (b) Romberg integration (Es =…

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Q: Beta Function : Evalnate the following integrals s a-4 dx I+x4 k, k b. (1- z ans. sin( ans: C.…

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Q: сер 3 Substitute the expressions for u and v in the integral. x cos 9x dx = x sin(9)x sin( x) dx…

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Q: Exercise 1: Directions: Evaluate the following integrals. Show your complete solutions. Identify the…

A: (3)

Q: Question 16 Consider parts? A B -S₁²x sinx dx. Using integration by parts, let u = e2x, dv = sinx…

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Q: 9 In order to evaluate the following integral 1 -√2/cos-¹(√x) dx 1 =- we first use the substitution…

A: Given: I=-∫12xcos-1(x)dx

Q: Q5/ find the integration (answer five only) 1- S(2x – 5)/3x – 1) dx | 4 2- S, S(x³ – 10 + 3y² dy dx…

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Q: Using Simpson's 3/8th rule, evaluate the integration 10e x dx, n=3, h =1/3 3x-2 the result is AO…

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Q: [(1- sinx) dx cos'x sinx COSX cos?x %3D COSX %3D = |(sec2 secx tanx) dx = tanx - secx + c. ACAS a a…

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Q: 5. [-/1 Points] DETAILS LARCALCET7 8.3.043. Find the indefinite integral. (Use C for the constant of…

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Q: t = -1,t = 0,t =1,... 3. Verify the result shown using 'integration by parts'. 1 1 |t sin(nt) dt =…

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Q: 4. Let a >0 and b be real numbers. Use integration to confirm the following identities. integer. a…

A: As we know that the integration by parts is : ∫udv=uv-∫vdu

Q: a) [ „J: Evaluate the integral (4x + 1) In x dx b) ' . Evaluate the integral fou 6 tan' x sec* x dx…

A: a) Given:       ∫4x+1ln x dx Integrate by parts: ∫fg'=fg-∫f'g where f=ln x , g'=4x+1           f'=1x…

Q: COS X COS X dx = %3D 1 - cos?x xp Rewrite the right side as a product of two fractions and evaluate…

A: ∫ cosx1-cos2xdx...............(1) use the formula sin2x+cos2x=1 sin2x=1-cos2x…

Q: Homework: Evaluate the definite integrals A. (a) 5x dx (b),-dt (bL- dt B. (a)cos 2x dx (b 4 cos t dt…

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: Activity 2. Using U- Substitution or Integration by Parts, evaluate the Indefinite Integral of the…

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Q: Can you help with question 5

A: 5). To evaluate the integral. a). ∫01x35x4+2dx Let substitute t=5x4+2. Differentiating on both…

Q: 10. J =-2x+1)a dx Learning Task 3: Complete the table by identifying u and du for the integrals.…

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Q: xP-1 7. Find the relation between p and q that makes integralS dx con- 1+ x9 vergent. A) p=q B) q>P…

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Q: + oo Consider the improper integral dx . What will be an appropriate solution and answer? x2+ 2x+ 2…

A: We have to find solution of improper integral.