4 Calculate the integral: dr 9 x2 + 18 z + 18 4.

Q: Evaluate the iterated integral: , S (2x²y + 3ay") de dy.

A: The objective is to find the value of the iterated integral ∫-12∫242x2y+3xy2dxdy First integrate…

Q: Use the substitution formula to evaluate the integral 6r dr V16• 3r² O 2V19 -8 O NIS .4

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Q: Evaluate the integral. * 64 In(y) Ap Vy J49

A: To evaluate the given integral.

Q: Evaluate the integral, 12 sec(4t) dt 2+3 tan (4t) dt = 2+3 tan (4t)

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Q: Evaluate the integral. 7y 1-7y dy

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Q: Evaluate the double integral given by p2 sinOdrd0 TT JO

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

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Q: Calculate the double integrals 1. R xedxdy, R-[0,1]X[0,1]

A: To find the below double integral.

Q: 5. Determine if the integral is conve 0. exdx -1/2 V1-e 2x

A: Given query is to find integral converges or diverges.

Q: Evaluate the integral: , (V4-z² dydz O 2[1- 4] + c O 2 [1 – ±] et

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Q: calculate the integral of  integral of 0 to 4 for dt/64t^2+9

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Q: Evaluate the double integral : (2r + 2y – 4) d dz O 75 O 100 O 175 O 150

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Q: Evaluate the integral. inegral (3t -2 )/ (t+1) dt

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Q: Evaluate the integral. In(9 x - 8) dx =| +C %3D

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Q: Evaluate the indefinite integral ∫⟨4cos2t,4tet2,2t+3t2⟩dt.

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Q: Evaluate the integral 50 fa* (z* – 6)" de by making the substitution u = x* – 6. %3D

A: Given integral, ∫x3x4-650dx Evaluate by substituting x4-6 for u in the given integral.

Q: Calculate the indefinite integral: ∫ (9t−2/3 + 4t7/3) dt

A: Integration formulas help to find the integration of the given function. The integration formula…

Q: Evaluate the integral using FTC I.

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Q: Evaluate the integrals in Exercises 2. J 3 dx dx 1. 9 + x VI + 9x

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Q: Evaluate the integral. 1 ds V5s - 9

A: Given,         ∫15s-9ds

Q: calculate the 4-) integrals rdr a-) b-) (x2-9r+20)dr (-3)a

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Q: 6. Calculate the integral in parts: Je (2x + 4) cos(4x) da.

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Q: Find the integral 1 dt 4t2 + 4t + 5

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Q: Evaluate the integral da (7x + 10)2" by making the appropriate substitution: u = dx (7x + 10)

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Q: Evaluate the integral. 63e V7x 2 /x xp

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Q: "(2 - sinoy de

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Q: Evaluate the triple iterated integral. LLL Jo π/4 6 6-r rz dz dr de

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Q: (1 + 1)² – 1 , dt

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Q: Compute the given improper integral. Enter the exact value of the answer. 7 In(4x)dr 0,

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Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 * O 0.412 O 0.211 O 0.189 O 0.316

A: Evaluate definite Integral

Q: COSz Show, without evaluating the integral, that z2(z + 1) *26 5 zp-

A: Given integral is , ∫ccoszz2z+1dz. Cauchy residue test: ∮fzdx=2πib1. Where b1is residue of fz.…

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: Inx 2. S soe ye*dzdxdy

A: topic - triple integration

Q: Evaluate the following integral. ∫ 2z5e1-z dz

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Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: Evaluate the integral a"(2* - 3) "de, 19 by making the appropriate substitution: u = 19

A: The given integral is ∫x3x4-319dx

Q: Evaluate the integral 22V4 – 2² dz

A: Use the trigonometric substitution to evaluate the given integral. Also calculate the limits for…

Q: 20 + S 2c + 5 こ

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Q: Evaluate the double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

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Q: Evaluate the integral. r3 3 cosh(t) dt 30.05

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Q: Evaluate the integrals by subs;tu;on dp- V5+x c)

A: ∫-14x5+x dx

Q: V1+ vz dz

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Q: Evaluate the integral. 4 VE dt VE 4 Vi dt =

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Q: Evaluate the integral AP R = [0, 2] x [2, 4] × [-1, 1]. (y + z)2

A: As per the instruction, we will be solving only the first one.…

Q: What is the integral of (3t – 1)^3 dt

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Evaluate the improper integral or state that it is divergent. dt 2 - 3t 4-

A: Given that: ∫4∞dtt2-3t

Q: Evaluate the integral 22 V4 – 22 dz 0.

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Q: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: Evaluate the integral. 81 In y 64 Vy

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Q: Evaluate the improper integral : 6be 8z" dx

A: Note: As per our guideline we are supposed to answer only one question. kindly repost the other…

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.