Triangle with vertices (0,0), (-2,4) and (8,4) ey²+1dA

Q: Compute the double integral (86xy – x²) dA over the region bounded below by y = x², above by y = Vx.…

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Q: Which of the following integrals represent the area of the region in

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Q: Use a double integral to find the area of the shaded region.

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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: Calculate the area under the curve 4x2+1 on the integral , [0,4] n=4 using MRAM

A: Given f(x)=4x2+1, 0,4, n=4

Q: 1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

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Q: z=6-x-y Yy=4-x²

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Q: Evaluate the following double integrals over the given region R. (x+ y*) dA, R is the triangle with…

A: Sketch the region and range of x and y. Than integrate function.

Q: Calculate the double integral of f(x, y) = 4 – 8x over the triangle with vertices 0 = (0,0), A =…

A: Consider the function: fx,y=4-8x To sketch the triangle with vertices O (0, 0), A (3, 7), B (5, 7)

Q: Evaluate the following Triple integrals over the regions defined in the second column, if available

A: Let the given integral be I -I = ∫12∫02∫-112+z2-xydzdxdyIntegrating first with respect to z -I =…

Q: Use a double integral to find the area of the region one loop of the rose: r = 7cos(3θ)

A: Given : r = 7cos(3θ)

Q: change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor integral…

A: To change cartesian equation into polar, we use following substitutions x=r cosθy=r sinθdydx=r dr dθ

Q: 3. Evaluate the integrals by interpreting them in terms of areas a) L(1+ v - ) 22 – x2 ) dx, b) 3

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Q: Evaluate the double integral using single applications of Simpson's 1/3 rule 2 (x2. 3y2 + xy³) dx dy…

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Q: 3. Compute the following integrals. 2/5 (a) V4 – 25x² dx.

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Q: Compute the integral of f(x) = 0.4 – 2x² + 40x5 from a = 0 to b = 0.8 using i. Trapezoidal Rule with…

A: Numerical integration

Q: The region D is bounded by the curves y = 5, and y = 5x². Which of the following can be used to…

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Q: Compute the following integrals (a) Sial dz. Iz%31 z2+z+2

A: Take fz=1z2+z+2 Equating the denominator to 0, we get z2+z+2=0⇒z--1+7i2z--1-7i2=0 Hence…

Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

A: where are is the trapezoidal region with vertices(8,0),(10,0),(0,10), and (0,8).

Q: Evaluate the following integrals over the region A. b) || x²ydA, A:= triangle with vertices (0;0),…

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Q: compute the given double integral over the indicated rectangle. // by a – 2y° dA R= [1,4] × [0, 3] R

A: Given Integral: I=∬R(6yx-2y3)dA dA=dx.dy R=1,4×0,3 Limits of x are from 1 to 4. Limits of y are from…

Q: Compute the following double integral over the indicated rectangle (a) by integrating with respect…

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Q: Evaluate the following n-dimensional integral by Monte Carlo method II +3+.+2) dV (9.127) where the…

A: We have to use the Monte Carlo method, to find the value of the multivariate integral for : n = 6 n…

Q: Compute the following double integral over the indicated rectangle Yer -4x d A, R= [0,2] × [0, V8]

A: We are using Double integration here

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -9a In(z)…

A: Given : ∫-9xlnxdx

Q: Find Faurier's integral for 2く。 fcze) = K, oくe3 o, x73

A: Given: f(x)=0  , x<0x  , 0<x<30  ,  x>3 We have to find the Fourier's Integral for the…

Q: 4) Use Romberg integration to compute the following integral for n=3. 10 Te dr

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Q: | 7x2 V2x3 - 1 dx

A: Here the given integration I=∫7x22x3-1dxNow Substitute as2x3-1 =u⇒6x2dx=duThus the integration…

Q: Compute the following improper integral. dx

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Q: By using u = In x, evaluate the integrals In x dx.

A: ∫x-1xlnx dx Now put, u=lnx⇒dudx=1x⇒du=1x dx

Q: 2. Show that, in the region D: 0 < x<1, 0 <y< x², the following double integral 1 dA =- In(2) x5 + 1…

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Q: Which of the ff double integrals has bounds that represents the Region A a. b. y [ -6 y = 2x [ f(x,…

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Q: S(3x – 2)(x + 1) dx

A: First multiply the expression under Integral then integrate and put the limits

Q: Use an iterated integral to find the area of the region bounded by the graphs of y = 6x ² and y = ²…

A: Topic = Area

Q: 5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A: Given integral ∫12∫02x-x21x2+y22dydx. The objective is to evaluate the integral. First we change x…

Q: Compute each of the following double integrals over the indicated rectangles. 1 " JI (2x + 3y) d.A,…

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Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: E is the region below z = -3x² – 3y2 and above z = -12 I| 4y?dV E

A: Given triple integral, ∫∫E∫4y2dV Here E is the region below z=-3x2-3y2 and above z=-12. Evaluate the…

Q: Evaluate the following integral. JJ. xyz dV if S is the region bounded by the cylinders x² + y² =…

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Q: Evaluate the Foll aning integrals a) 32ペ-T Ax b) CSCXXX -1/4 TY3 Sinx よ× /3

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Q: 1. Compute the following double integrals over the indicated rectangles. (a) // (6y V – 2y) dA, R=…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...

Q: Set up the definite integral that gives the area of the shaded region bounded by the graphs of y,…

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Q: Evaluate the following integrals over the region A. 2) |/. d ey dA, A:= triangle with vertices…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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.