1. Find the exact value of the iterated integral by changing the order of the integration: 8 2 1 dxdy in 1+x

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: 1 dx х6—х

A: To evaluate the integral: ∫1x6-xdx Solution: ∫1x6-xdx On simplifying further we get:…

Q: e17z In(23z)dx By applying integration by parts to the integral we obtain

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Q: Calculate the iterated integral. 36 LTC + ar X dx

A: Solve the following

Q: Evaluate the following integral by reversing the order of integration: integral 2 0 integral 1 y/2…

A: Given:-               I = ∫02∫y/21ex2dxdy

Q: 14 Find the integrals using integration by parts. a. fx(x + 4)°dx c. fr'e"dr

A: As per our guidelines I am solving only first three parts of the question please resubmit the other…

Q: 4 dx, u= 1 + 2x (1 + 2x)

A: Explanation: Given that: ∫41+2x3dx,      u=1+2x Concept: 1. ∫xndx=1n+1xn+1+C Calculation: First…

Q: Evaluate the iterated integral by choosing the order of integration. e( 4x In(y) Зy In(x) dy dx

A: We have to compute the double integration

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) yV 6 +…

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Q: Evaluate the integral. (Use C for the constant of integration.) dt 1- t10

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Q: Evaluate the integral. (Use C for the constant of integration.) | 3x2 cos(mx) dx

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Q: Use Romberg integration to compute R3,3 for the following integral x sin x dx

A: Given integral is, ∫01xsinx dx Then, h1=b-a=1-0=1h2=b-a2=12h3=b-a4=14

Q: area ZA (xy) dx dy y/3 10.

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Q: Consider the integral sin(5z) d: Applying the integration by parts technique, let and du x dz Then…

A: The by parts formula of integration is ∫udv=uv-∫vdu.

Q: 2 4-2y 4x-x dxdy r2y 4x-x dxdy + e e

A: The reverse Order integration is:-

Q: Evaluate the iterated integral by converting to lar coordinates. /1-(х-1)2 x² + y² dy dx

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Q: In 4 r4 1 dy dx ex In y

A: We have to evaluate the integral                                      ∫0ln4∫ex41lnydydx The region…

Q: Evaluate the iterated integral given below

A: The given question is from the calculus and subcategory of the double integration we can solve this…

Q: Reverse the order of integration in the iterated integral and then evaluate the integral. NE p2-x*…

A: The region of integration is

Q: Use Romberg integration to compute Rg,3 for the following integral x sin x dx

A: Given integral is, ∫01xsinx dx Then we can write as, h1=b-a=1-0=1h2=b-a2=12h3=b-a4=14

Q: Evaluate the iterated integral [² [² 2e3² dy dx by changing the order of integration.

A: The given integral is ∫02∫x22ey2dy dx In original integration, the integration order is dy dx. Our…

Q: dx '1 x[13+ln(x²)]

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Q: Reverse the order of integration and evaluate the following integral. 2ex2 dx dy 1 c1

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Q: V2m + 13 e dm

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Q: Evaluate the integral using tabular integration by parts. | (5 2² – x + 1) e¯* dæe +C

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Q: In(x) d. f(x,y)dydx 1

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Q: Use Romberg integration to find an 0(h*) approximation for the following integral I = In(x² + 3)dx

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Q: Use a double integral to fi and y = 3(x+ 1).

A: Given the two curves y=x2+2x+1y=3(x+1)

Q: Reverse the order of integration in order to calculate the following integral: 2 1+x4 0 dx dy.

A: We can evaluate the given integral by using the integral formulas.

Q: Evaluate the iterated integral given below

A: Given: Let I=∫120∫0π6e2y sin3xdxdy To Find: To evaluate the given integral.

Q: Use the substitution technique to determine the following integrals:

A: Let,

Q: 1. dx (т + 1) (2 + 1) 1

A: Explanation of the answer is as follows

Q: To find the definite integral Vx2 + 64 dx, apply the basic integration rule. Let u = x2 + 64.…

A: We have to find the definite integral. Here we are using integration by substitution.

Q: Write the iterated integral ∫10-10∫200 (x2y + 2xy3) dy dxwith the order of integration reversed.

A: To evaluate: ∫-1010∫020x2y+2xy3dydx. Evaluating the integral.…

Q: Evaluate the iterated integral by choosing the order of integration. 4 In(y) + dy dx /1 2y + 1

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Q: ∫ (e3x+5ex+2  divided by  ex) dx a.) Compute the integral

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: We have to solve the problem

Q: Evaluate the integral using integration by parts 1. J xe" dx;

A: Given : Dear student as per our rule in one session we can only solve one question. Please post the…

Q: dx 1 = J Jaz-x2

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Q: 4. S x² e*dx

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Q: Calculate the following integrals. (०) / जरेगार dx dr (b) */4+(In r)?

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Q: Evaluate the given integral with suitable substitution: (42x + 42) dz

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Q: 2. Evaluate the integral by switching the order of integration: Sy e" dædy.

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Q: 8. Evaluate the integral by using a substitution prior to integration by parts. xp- Vx² + 18 - 9 m…

A: Given query is to find the value of the integral.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: Reverse the order of integration in S(2xy + 1)dxdy and then evaluate.

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Q: Evaluate the integral. (Use C for the constant of integration.) 16 In xp (x^ +C

A: Topic:- integration

Q: Evaluate the iterated integral by choosing the order of integration. 1 x + 3y xe* dy dx

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Q: Evaluate the integral using integration by parts. [8 e 20 sin 20 de

A: The formula for the integration by parts is ∫udv=uv-∫vdu The given integral is ∫8e2θsin2θdθ

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.