Q.1) Evaluate the following integral 2dx x (3(ln z)2 + 12 In r- 15)

Q: Q1 - Evaluate the following integral: J (2x2-3x+2) dx (x-1)2 (x-2)

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Q: 11. Evaluate the following integrals: (a) 2+ 2- dt 1/2 (b) ["a 1 dt 2. (c) I12-x| dx

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

A: a) ∫1e1+ln x2xdxb) ∫-1112x+3dx

Q: 2. Compute the following definite integral: X-3x+2 dx x2-2x

A: The solution is :

Q: Compute the given indefinite integral. fir (2 – 4)(x + 3)dæ | +C

A: Given integral, ∫x-4x+3dx

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

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Q: 2. Use the Definition of Residue to show that: dz -ni Izl=1 z² sinh z 3 Where 0 < |z| < T.

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Q: Evaluate the following integral: [²√²+² (cos(x² + y² S - y²)) dydx

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Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: Given: ∫t8 t9-149 dt Solve the integral. Method of solving: Substitution Method. Formula used: i)…

Q: Evaluate the following indefinite integral. 7 1+8t -dt 5t (Type an exact answer.) √ 1+8t 5t -dt=

A: The given integral is ∫1+8t75t dt

Q: 19. fy/6 + 4y – 4y² dy

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Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: x 3*dx Jo

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Q: 6. Evaluate the following real integrals by residue theorem 3 ーン ans : 493 • I= ST dX ans 8 12…

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Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: Evaluate the following indefinite integral. 1 √ 3 ² + 8 - t dt =

A: Given.

Q: Evaluate the indefinite integral. 3 dt (t + 8)5 + C

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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 integral. 7 7 √49-x² ILL 1 /49-x² (x² + y²)1/2 dy dx dz =

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Q: Evaluate the indefinite integral. (Use C for the cons x(2x + 5)8dx

A: Integration of x(2x+5)8.

Q: Find the indefinite integral. 4x2+2x-1 d.x none of these Omz + 1| -31m|z미-글+C o+ Inz* + =*|+C In a+1…

A: Given: I=∫4x2+2x-1x3+x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And…

Q: Find the indefinite integral

A: Given: ∫t1-t4dt

Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0&lt;z&lt;π…

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: 11 By reversing evaluate the -3 -9 ffix the orders of integration following integral x cos(y) dy dx

A: Given integral ∫03∫x29 xcosy2dydx The region bounded by  y=x2 , y=9 , x=3 and x=0

Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: Evaluate the definite integral. •4 ti + t?j| dt 3 |(7 - 1) 2 17 3 173 3

A: The value of the given integral is 1/3(173/2 - 1)

Q: Find the indefinite integral.

A: Consider the given integral ∫2-1tt2dt

Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

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: 6.3.18. Evaluate the integral. using U substitution integrate (cos^2(x)sin^2(x))dx

A: Hello, there are two functions present in the question. As the first function comes along with the…

Q: Q.1) Evaluate the following integral 2dr (3(In r) + 12 ln z -15)

A: Given:∫2x3ln2(x)+12ln(x)-15dx=23∫1xln2(x)+4ln(x)-5dxNow solving∫1xln2(x)+4ln(x)-5dxsubstitute…

Q: Evaluate the definite integral. 2 St³√₁+t² dt 0

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Q: Evaluate the improper integral t* e-2t 3+e-4t at

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Q: z'e? dz

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Q: 9. Evaluate the indefinite integral x'V4-x² dx . 3 Hint: Let u = 4 – x² and write x' = xx?.

A: Given ∫x34-x2dx

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

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Q: 2 2. Evaluate the iterated integral 6x'y dady

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Q: Q1 - Evaluate the following integral: J (2x-3x+2) dx (x-1)2 (x-2)

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Q: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

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: [4] 5. Use the fact that 1 +C 4e2r dx = 2e2 to either evaluate the improper integral 2 dr, or show…

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Q: Evaluate the integral. 1 8 dt V15-21-? - 1 OA. 6 В. O C. 4 D. 3" O D. co fm

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Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: 2 Evaluate the definite integral Зх + 4 dx 11 5 17 17 2 ךי" יזנ 3.

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Q: (8) 18. Evaluate the following indefinite integrals: (a) / (5e* +7z + 1le") dr dr

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Q: 1. Evaluate the integral using the given substitution xcos(9x2)dx u = 9x2

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