Evaluate the double integral / ydrdy where T is the triangle with vertices (0,-1), (0, 5), (4, 3).

Q: Evaluate the Integral iF the funthun X = = XSin (xy) ニ over the vecfongulor region R- [0,1][1, 2]

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Q: U V3-22- zt

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Q: Evaluate the integrals in Exercises 69 : (2r – 1) cos V3(2r – 1)² + 6 -dr V3(2r – 1)2 + 6 69.

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Q: use a computer algebra system to evaluate the triple iterated integral.

A: Using a calculator we get:

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

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Q: Compute line integral of F(x,y) = (2x² – 3,₁²³)^² + (2x +34²) ↑ с over the following C F-dr SCF ¾ ç…

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Q: I, FIND HE NET AREA OF fos) - Zx and gx)= O FROM [-3,3]

A: Given : Functions f(x) = 2x and g(x) = 0   To find : Net area of f(x) and g(x) from [-3,3]?

Q: 5) Evaluate the integral.cusc c for the constan6 of integrafion) 2(ean cx) +6an cx>) dx

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Q: Use symmetry to evaluate the double integral. 2xy J63 JR 1 + x ,10 dA, R = {(x, y) | -4 ≤ x ≤ 4,0 ≤…

A: Consider the given double integral, ∫∫R2xy1+x10dA, where R=x,y-4≤x≤4, 0≤y≤1. Consider the integrand,…

Q: Use Green's Theorem to evaluate the integral 3x²y²dx + (5y³ – x³y²)dy, C

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Q: Obtain the moment of the area generated by x = 2a, bounded by x =y and x2 = 2av.

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Q: By converting the integral I- rdrd® into Cartesian coordinates, we get:

A: Here we will assume coordinates for converting polar to cartesian. x=rsintheta y=rcostheta…

Q: Use substitution to change the integral (3x + 4y)dA over the parallelogram with corners (0, 0),…

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Q: Compute the double integral , xy³ dA where T is the triangle (-1,0), (0, 5), (1,0).

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Q: 9. √√4-4x² Convert ₁42(4-4x² - y²)dydr into a triple integral with dV = dydzdx. C

A: Given :∫-11∫-4-4x24-4x24-4x2-y2dydx and dV=dy dz dx To convert the double integral into triple…

Q: (a) Solve the line integral yzdx - xzdy + xyzdz on a particle that moves along the line segment from…

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Q: Evaluate the integral 1 / / emax{x²,v²} dydx

A: integral of  ∫01∫01emax {x2,y2}dydx

Q: 15. Evaluate the integral zVx² + y²dzdxdy by using cylindirical coordinates.

A: I have Provided this answer in step-2.

Q: Evaluate the iterated integral: dydx - 1/4 Jx2

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Q: a) Find the triple integral xdV.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: hat is the integrable form of J JcoE e sin sin(0) do cos 1– u² du sin 2 – 1 du s(u) du

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Q: In Exercises 5-40, evaluate the integral using FTC I.

A: we have to evaluate the value of the definite integral ∫04ydy. let the given integral be I.…

Q: Evaluate the im proper integral dx 3 (5-2)

A: Given integral is: I=∫05dx(5-x)3 Let us assume f(x)=1(5-x)32 Here x=5 is the point of infinite…

Q: Evaluate the integral. VZ/2 dr V1-2

A: In this question we have to evaluate the Integral.

Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: 4. Evaluate the iterated integral: dydx. 1/4 Ja2

A: The solution are next

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: 4) Write the integral to calculate the outward flux through F = (-yx2, xy,-z) across the sphere with…

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Q: What is the integrable form of et dr? ex – e -x [(1-u²) ² du O Swi-) - 1) 2 du (1- " (D 2 du

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Q: Evaluate the integral (2³ + 1)'/³,³dx.

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Q: Evaluate the line integral S. 4x²ds, where C is the line segment from (-2, –1) to (0,–1) followed by…

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Q: Solve the problem in a paper and upload as a pdf document. .3 Evaluate the integral SIT w?yz+v² xz +…

A: Solution: The objective is to evaluate the given integral

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: + 1 -оу-х -oy=x2

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Q: What is the integrable form of dr? du u du

A: Given integral is:

Q: The improper integral 3dx is /1->

A: Given:⇒∫013dx1-x2⇒3∫11-x2dxWe know that ∫11-x2dx=sec-1(x)

Q: Use the double integral to find the area of R where R is the triangle with vertices (-4,0), (2,0),…

A: Definition used -          Area using double integral -                 A=∫ab∫f(x)g(x)dydx…

Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

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Q: Evaluate the integralt uie dr using the two-point Gaussian quadrature rule. 1416z | e - je 0 O o o O…

A: For the integral I=∫abf(x)dx, the Gauss quadrature 2-point formula is, I=b-a2w1fm1+w2fx2 where…

Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: 9. Convert ¹42(4-4x²-y²)dydr into a triple integral with dV = dydzdx.

A: Here we conside the limits of x nad y then we try to find the limit of z for which after integrating…

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 integrable form of dr? 1 -1) du -u?) 2 du 2022-01..

A: Find the integrable form by substitution method

Q: Evaluate the integral: (In z)6 dz %3D

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Q: Write the integrand in terms of u. 2x (x + 1)' dx = du %3D Evaluate the integral.

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Q: Evaluate the lino integral y+ + (4+2-x>y +2が Where C consitts of line segments from 0,-,2) to…

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Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.

Q: Evaluate the integral: æ V81 *Vs1 – z'da -

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.