Evaluate the integral: ∭D(x2+y2+z2) dxdydz, where D is defined by x2+y2+z2≤2.

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: Evaluate the integral using appropriate substitution. an V3- a de + C

A: It is required to evaluate integral by substitution.

Q: 2x Evaluate the improper integral J da, if it exists. (z² + 121)?

A: Use the substitution method of integration

Q: Evaluate the integral , f(x) dx, where 3 — х3, х 1

A: Given a piecewise function We need to find integral from x=-2 to 3

Q: Use the Table of Integrals to evaluate the integral. (Use C for the const 6 + 12y – 36y2 dy 3 + ( 6y…

A: Given ∫y-36y2+12y+6dy⇒6∫y-6y2+2y+1 dy⇒∫y-6y2+2y+1dy , write y as 16-1122-12y and…

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

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Q: Evaluate the integral below, where H is the solid hemisphere x² + y² + z² ≤ 4, z≥ 0. SSSH (4x² - y²)…

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Q: Express the integral in terms of the variable u, but do not evaluate In a u= In a In r du %3D

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Q: Evaluate the integral by making the given substitution. sec(6z)tan(6æ)dr, u = 6z + C

A: According to question given :∫sec6xtan6x dx, u=6xWe have to evaluate the integral by making the…

Q: Evaluate the integral da 2+ et using the substitution u = 2+ eª. dx 2+ et +C | -

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Q: Calculate the integral f. (z-2)²2 dz, where C: |z – 1| = 3.

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Q: Evaluate the integral by making an appropriate change of variables. 9(x dA, where R is the rectangle…

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Q: Evaluate the integral SSRe-(²*+y°)dA, where R is given by x? + y² 0. е

A: We will answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Evaluate the integral by making the given substitution. dp, и %3D 1 + бр2 1 + 6p2 + C

A: Solve the indefinite integral in the following way:-

Q: Evaluate the integral of f(x, y) = xy over the shaded domain D. (Assume that a = 6.) IL wen - O a2.…

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Q: Evaluate the integral. dA, R X + 1 R = [0, 9] × [0, 8]

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Q: Evaluate the integral using the given substitution. 18(6x- 2)6 dx , u = 6x - 2 0.(6x - 2) +C O (6x -…

A: The given integral is ∫186x-2-6dx and  u=6x-2

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: Evaluate the improper integral (A) diverges (в B (C) ml+ 2 3 √√2²233/3dx 4

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Q: The integral from a to b of f(x) is denoted by_____

A: Given, To fill the blank The integral from a to b of f(x) is denoted by_____

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

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Q: Express the integral in terms of the variable u, but do not evaluate it. In x dx; u = In x re23 In x…

A: Topic:- integration

Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

Q: Evaluate the integral. r 81 In(y) dy Vy 64

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Q: Evaluate the integral. r81 In(y) dy Vy 64

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Q: 7 dx. J 2+ Vx – 4

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Q: Calculate the integral f. dz, where C: |z| = 1. (2z+1)(2-2)

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Q: dx (x + 2)3

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Q: Evaluate the integral using the given substitution. Sx4x5 -s;² dx , u =x5 -8 * - 8) + C

A: We have to solve given integral by substitution.

Q: Evaluate the integral f 2x (x² + 2)° dx using the substitution u = x? + 2. | 20(a* + 2)" de +C

A: The given integral is: I=∫2xx2+26 dx

Q: Evaluate the integral, if C is the circular path y = (1-x^2) from (1,0) to (0,1).

A: Let y=1-x2 be circular path from (1,0) to (0,1). Parameterize the above path by taking x=cosθ , then…

Q: Evaluate the integral by making the given substitution. | x³(7 + x4)7 dx, u = 7 + x* (7 +x^)4 + C 32

A: Given ;

Q: Evaluate the integral Ja (2 – 4)°dæ (x³ – by making the substitution u = x° – 4.

A: Consider the given integral

Q: Find the integral using the substitution u = t3.

A:

Q: Evaluate the integral Ja (2 – 2) " da, - by making the appropriate substitution: u =

A: The given integral is ∫x2x3-219dx

Q: Rewrite the iterated integrals in the order dzdyda 11-y? 1-y SS Sf(,y, z)dadzdy 0 0

A:

Q: Evaluate the integral ff, (x + y) dA, where R = {(x,y): 1<x² + y² < 4, x< 0}. %3D

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Q: Use the Trapezoidal Rule to evaluate the integral S |r| x²dx O 2 O -2 O 1 -1

A: Given Intergral ∫-11xx2dx. We have to find the value of it by using the Trapezoidal Rule. The…

Q: Evaluate the following integral, where R is bounded by x= 2, y = 3x + 3, and y = -x- 1. y? dA R

A: We can think of this region as y ranging from -x - 1 to 3x + 3. and x ranging from -1 to 2.

Q: Evaluate the double integral + 2y) dA, where D is bounded by y = x, y = = x°, and x > 0. 3 Answer:

A:

Q: Compute the double integral of f(x, y) = 45xy over the domain D. D: bounded by x = y and x = y2 45xy…

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Q: The result of the integral in 0 given V Vr²- 25 -dy is 5 tan0 -50 +C, True B False

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Q: Calculate the integral, assuming that o' f(x) dx : = -4, f f(x) dx = 2, f* f(x) dx = 11. %3D

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Q: Evaluate the improper integral dz, if it exist (x² + 49)2

A: Here we have to evaluate the given improper integral.

Q: Use integration by parts to evaluate the integral: 3. In(r) dr r8 .020327 %3D

A:

Q: ds :? V5s+6

A: We use substitution method to solve the given integration .

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.