The value of the improper integral / 36 z² e ² dz = 12e1 O - 36e 1 O 36e 1 O 12e 1

Q: Evaluate the integral fa* (2* – 11)"dz, dx, by making the appropriate substitution: u = 11). 24 dx =…

A: ∫x3x4-1124dxSubstitute u=x4-11du=4x3dxdu4=x3dx

Q: 2- Evaluate the integrals in Exercises 7- 8- 9- In 9 Son 24/2 In 4 S dr [ 21 e ² dt ex/2 dx

A: To evaluate the given integrals.

Q: 12. The integral of dy S Sec-' (5 ) + C 3 O ţSec-"' ( ) + C 3 Sin-l (플) G) +c 3 o Sim' (등) +C O…

A: This is based on simple formula of integration

Q: Solve the triple integral I| (x² + y² + z²)7/2 dV where B is the unit ball B O 2n 2л О Зл 5 o 7n 5 O…

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Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

Q: 3. a. Use a computer algebra system to evaluate the following integrals. i. : / Inz dz i. / 2 ln z…

A: The solution are next step

Q: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

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Q: 10. Evaluate the integral ffS (xy + z²)dV, where E = {(x,y, z:0 Sx< 2,0 < ys 1,0 <z< 3)} using three…

A: given , integral ∫∫∫xy+z2dV  where E=x,y,z:0≤x≤2,0≤y≤1,0≤z≤3 claim- to evaluate the integral

Q: Evaluate the iterated integral. In 4 In 3 e 2x+Y dy dx 0 1 In 4 In 3 | | e 2x+ydy | dx = 0 1 (Type…

A: Solve the following integral

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

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Q: T 3. fz sin4 y cos7 y dy 2

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Q: In approximation of f(x)dx by Romberg Integration, if R, =0.25 and Ry =0.2525, then R= O None of…

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Q: The value of the improper integral 42 x² e¯¤* dx 1 - 14e 14e-1 - O 14e-1 O 42e-1 O – 42e-1

A: Explanation of the solution is given below...

Q: Q.3 Find the double integral for Sle x² dydx, where R between y = -4/x y = -x and x = -4

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Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

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Q: Evaluate the improper integral. 16 16 dy dx Vx + Vy 0 0 256 O A. 3 (1- In 2) 64 O B. (1- In 2) 128…

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Q: 5- The value of the integral J. (Z+1)4 Where C is Z = |3||

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: -2 2 7e" + dy -5

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Q: calculate the result of the following integrals Sinł dz 19423,2 A) IZI 22 Z +4 dz IZI :4…

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Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: Evaluate the iterated integral. In 3 In 2 x+2Y dy dx e 0 1 In 3 In 2 e**2Ydy dx= X+2y 0 1 (Type an…

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Q: 3. S (5y-4)dy y³+4y²

A: We know, ∫dx/x= ln|x|

Q: Evaluate the 2 improper integrals attached with this question.

A: Given integrals are

Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

A: Since, you have asked multiple questions, we will solve the first question for you. If you want any…

Q: We'll now apply the integration by parts procedure to the new integral e70 cos(80) d0, letting U =…

A: The given integral,∫e7θ cos(8θ) dθ

Q: 3 by taking n= 6 [In x · dx solution of the integral with Simpson's • method 3. (y, + y2 + y4 + y3 +…

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Q: 21 Which of the following integrals is equal to the integral | s(3x - 5) dx? (A zp (2)/ 7/3 (B) s(:)…

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Q: e the method of u-substitution to evaluate the given integrals. 4t dt 2 – 8t2

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Q: One of the following is an improper integral. - In 3 e* dx 4 – ex dx In 2 xV16 – In x dx cln 2 dx x…

A: In this question we have to find the value of Improper Integral. Note: As per our policy we are…

Q: ne following integral 2dr J r (3(ln r)2 + 12 In z- 15)

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Q: Evaluate the integral. S yz dx dz dy 0 2 2 O 128 3

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Q: 1) Calculate the following integrals: 1. S (5 +2)“ dz 2. fxe-a*/4 dx 3. S2-YE do x²– + Vx? 4. Sda…

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Q: 3z+4 dr Use the appropriate substitution to evaluate the following integrals: e %3D O e3a+4 + C ©…

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Q: Solve the double integral J, J, (1+ xy)² dydx In n(금) O 2ln(5) – In(3) O In(3) – 4ln(5)

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Q: A integral a° (1 – a² )dæ, após a mudança de variáveis æ sin(0) é expressa por

A: Given:∫01x21-x2dx

Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: 2. Evaluate the integral 8- (a) L« (4t5/2 – 3t3/2) dt (d) 2 - Vt dt r4 (e) t2 cos e de JT/4

A: The objective is to find the values of given integrals

Q: Evaluate the iterated integral. In 3 In 5 SS 3x+2y dy dx e 0 1 In 3 In 5 || 3x+2Ydy dx= 0 1 (Type an…

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Q: 2. Evaluate the following integrals. et a. (e2 +3)Ve2 – 16e-2" + 6

A: Solution

Q: S( z +1) e2² dz

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Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: Find the integral ſ cos³0 sin 0 d0 . Tentukan integral f cos³0 sin 0 de. 1 cos*0 + C 4 1. O 1 -coste…

A: Let's find.

Q: The value of the triple integral (x² + y²)dV where E is the E portion of x² + y² + z² = 4 with 0 ≤ y…

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Q: Q2:Solve the integrals as in below: 2-3y a² +b2 dy 1- j 2- S 3 (7* (7-3y 2)2 dy 0.5 2y 3- S -1 7 + e…

A: (Solving first three subparts as per our guidelines) Solution: 1.∫01yy5+1dy Now, ∫yy5+1dy…

Q: Evaluate the integrals et + 2e²' – e' dt e' dt 39. 40. e21 + 3e' + 2 e21 + 1 cos ydy sin? y + sin y…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. How would you begin to numerically approximate the double integral: bd 1-SSS(x.y)dxdy ac

A: Given integral is   I=∫ab∫cd fx, y dx dy

Q: Evaluate the iterated integral. In 5 In 3 4x+2y dy dx e 0 1 In 5 In 3 | 4x+2y dy dx = 0 1 (Type an…

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Q: Consider the indefinite integral (5x³ + 4x? 73x – 52 dx 16 Then the integrand decomposes into the…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.