1. Evaluate the following integrals * () dr cos (b) e cos 2r dr (c) +1-2 dr r2 +x - 2

Q: Compute the definite integrals. Lx cos(x) dx х COS OT – 1 O1 -2 O 2

A: Please refer the attached image for complete solution.

Q: Calculate the following integrals. (5D) 0.5 Los xin(x + 1) dxr -0.5 A)

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: 1 Determine the following integrals: ļ (cos2x+ sin x) dx 1.1.1 .1.2 1.1.3 1₁ Jx Xx+1 √√x²+2x+1 dx…

A: Given integrals, 1.1 ∫(cos2x+sinx)dx 1.2. ∫x+1x2+2x+1dx 1.3. ∫eln(3x)+2x+1dx The objective is to…

Q: ) Evaluate the integrals of the following; i) ,( + cos x)dr 1+cos 2t dt ii) 2 iii) [(3x +2)(3x?…

A: Given that:                           NOTE: As per our answering guidelines, we can only answer 1…

Q: 1. Compute the following integrals. (a) dx. (b) 2° sin(x³) dx.

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Q: 3. Find each of the following integrals using any suitable techniques : sin 2x dx cos4 2.x (c)

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Q: 1. Find the following indefinite integrals (any 4) +3x ii) [(2{/x* - 7x' +10e* – 1)dx iii) [(x²…

A: To evaluate the given indefinite integral.

Q: 1. Compute the following integrals. 1 cos 3x dx b) VAr + 7 c) a) dx dx sin x / (In x)3 f) / d) ſ eª…

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Q: Evaluate the integrals in ∫2ey cos ey dv

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Q: Evaluate the following integrals: 2. Inx de sin 3x 3. dx 1-cos 3x 4. S 32* dx 5. S(e* + 1)°e*dx 6.…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 8 cos" 2πt dt

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Q: 4. Evaluate the following integrals cos 3x - dx а) (x² +4)² do b) 5-4cos0

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Q: 1 6. Evaluate the given integral using suitable substituion COs(V도+ 3) dr

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Q: 10. Evaluate the definite integrals by u-substitution. In5 Te(3-4e) de ( 2 cos 3x dx b. а.

A: a. ∫0π62 cos3x dxb. ∫0ln 5ex3-4ex dx

Q: 3. Evaluate the integrals: S³r[cos(2x) – sin(3x)] dx С. 6 c1 dx d. Jo x2+1

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Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: [sin(In x)+cos(In x)]¯ dx

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Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: Q1. Evaluate the following Integrals 1 dx 1- cos x .2 +x - 2x +3 dx

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Q: 5. Evaluate the following integrals: sin x (1) f dx (ii) [Vsinx cos xdx (iii) -x' dx x* +3x? +2 V1+…

A: Dear student,                      According to our guidelines we are supposed to answer only first…

Q: 1. Evaluate the following integrals. sin x – 2x3 1+ 2x dx (b) 3+ x x3 + x dx (10 cos x + 5x4)5

A: to find the following integrals

Q: 2. Evaluate the following integrals. 6 a) dx x² – 3x b) | 4.2? cos(x³ + 2) dæ 4x2 c) / 4x² ln x dx

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Q: 1. Evaluate the following integrals: S; dx -x² + 4x - 3 f) . dx (x − 2)√√x² − 4x + 3 -

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Q: 1. Compute the following integrals. (a) sin (e) dx. 4 dx. - (b) x2

A: we have to calculate integration

Q: (cos 3t)²dt

A: The given integral is  ∫cos3t2dt. We also know that, 2cos2x=1+cos2x.

Q: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint:…

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Q: Evaluate the following integrals.

A: To integrate: ∫0π2e-3xcosxdx Use integration by parts:      ∫u dv = u v - ∫v du Let   u =cos(x)…

Q: 5. Evaluate the following improper integrals (if not shoW Wny). x² dx a- 00 4 1 dx -2 x+2 b-

A: To evaluate the improper integrals.

Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: 1) Find the integrals: i) i) SF Inx dx 4-X2

A: Part i          ∫x2-14-x2dx

Q: 2. Evaluate the following integrals. (a) J sin° (2) dæ 3x2 + 2x + 7 (b) dx x² + 1

A: We have to solve the given integral.

Q: Evaluate the following integrals: a) sin^4 (2x) cos^7 (2x) dx b) t sin^4 (t^2) dt c) tan^3 (x) dx d)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1. Compute the following integrals. (a) dx. (b) x³ sin(æ³) dx.

A: We have to integrate both

Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: 9. Evaluate the following integrals а. se cx b. CO s x + co s(8z) – iz 3 -4x с. dr x? +1 -

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Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

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Q: 4. Evaluate the following integrals: a) (22x +5e-*)dx b) S(esecnx sec Tx tan x)dx -In 16 e*/4

A: # we are entitled to solve one question at a time  please resubmit the other questions if you wish…

Q: 9. Calculate the following definite integrals by hand. (a) x² + 4x dx (b) cos(x) dx (c) o JE 3 dx

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Q: 4. Evaluate the following integrals: a) (e2x +5e-x)dx b) S(esecnx secпx sec Tx tan IX)dx c) Sin 16…

A: Evaluate: a∫e3x+5e-xdxb ∫esecπ xsecπ xtanπ xdxc ∫0ln16ex4 dx

Q: 1) Calculate the following integrals. b) √₁6x²=1 -dx

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Q: 1. Find the following indefinite integrals (any 4) (2/x* - 7x' +10e* – 1)dx (x* + 1)e* iii) dt +3x…

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Q: 1. Determine the following indefinite integrals: S (Ax-1 - Bx-3 + Vx") dx a) ez (wt) – cos(Ewt) )…

A: A=2.6, B=6.4, C=2.6, D=3.4, E=2.7 To find:-

Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: 1. Evaluate the following integrals. 3r5 (a) / dr V2 – x3 2" + e2" sin(2") sin(2=) dx 2x +3 (c) / dx…

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Q: 1 4 dx 2 /1 – x²

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Q: /4 1.* Use the following property of the definite integral to estimate the definite integral:JCcos x…

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Q: 1. Compute the following integrals. (a) 9¤ sin (e³¤) dx. (b) dx. x2 (c) + 4 dx. (Be smart.) x² + 1

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Q: 5. Evaluate the following integrals 3 sin #Z dz, c 1z-il=2 24 -4 ans: 3 co shz

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Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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