z=6-x-y Yy=4-x²

Q: Determine the value of the integral Integral sign: ((z^2 + r^2)^-3/2)x((2r)dr)

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Q: Find the integral [((a+1)x+(b+1))((c+1)x+(a+2))*** dx .

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Q: of the integrals 2- S S dA (1+x2+y2)ž Ris the top half x^2 + y^2 = 1 upper.

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Q: Calculate the integral ∫dx / √(x−a)(b−x).

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Q: Evaluate the double integral Is- (2 - 2 2) dxdy where S is the region in the 4th quadrant (y <0, z2…

A: Given the double integral and equation of curve I=∬Sx2−2x3dxdy And y−3x,y=−2x2

Q: Evaluate the integrals: B:S, S' S'(x² + y² + z²)dz dy dx

A: ∫01∫01∫01x2+y2+z2 dz dy dx

Q: Evaluate the given integral by making an appropriate change of variables, where R is the trapezoidal…

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Q: y²dy (y²+16)3/2

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Q: The improper integral A e B C) O D 1 if the 0 ∞ ex dx is

A: Solve the integration  From 0 to ♾️ for the integrand e-x.

Q: The area of the region outside the curve r=2+2cos0 and inside the curve r=3 is given by which…

A: Intersection points between two curves; r = 2 + 2 cos θ and r = 3 3 = 2 + 2 cos θ 1 = 2 cos θ cos θ…

Q: Evaluate the double integral || x(1+y²)¬1/2 dA; R is the region in the first R. quadrant enclosed…

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Q: The sum 5 f(2) dz + [ " f(2) dz - [, (=) dz can be written as a single integral in the form f(x) dz…

A: Please refer the attached image for complete solution.

Q: Sketch the region whose area is represented by the definite integral. dx y 12 12 10- 10 8. 6 6 10 2…

A: The definite integral can be used to evaluate area of region bounded by curves. If over an interval…

Q: +4)(v² +®y)Vy? +8y – 1 dy 3.

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Q: The definite integral that calculates the area of the shaded region is given as (4, 2) x= y² y = x-2…

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Q: Evaluate the integral directly by integration with respect to x and y. 7 x=(y/5)+1 5x-y S S dxdy…

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Q: Evaluate the integral (by interpreting it as the area between two curves) 4 I Va +2 – a| 0 dx -

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Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

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Q: Q5 Evaluate the integrals || (2.x+ y– 3)dA where R is the region as shown in the figure: - (i) 1 x=…

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Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

A: The integration formula for ∫xndx=xn+1n+1+C

Q: Set the double integral that will solve its area and evaluate the iterated double integral, SS, f(x,…

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Q: Evaluate the double integral on the given region. // (6xy²) dA; R:0 < x < 1 and x³3 < y < Vã R

A: we have to evaluate the double integral on the given region.

Q: T/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5 - 10

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Q: sketch the region of integration, and write an equivalent double integral with the order of…

A: Consider the following double integration: ∫01∫1-x1-x2dydx Region of integration: y=1-x2y=1-x

Q: Set up and evaluate the integral for finding the area and moments about t y = x2 - 25 y = 0 A = dx =…

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Q: Q5 Evaluate the integrals [[(2x+y-3)dA where R is the region as shown in the figure: R (i) (ii) 1 R…

A: 5 We have to evaluate ∬R2x+y−3dA, where R is the given region. i Consider the following figure.…

Q: se a double integral to find the area of the specified region. y y = 1 8 21

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Q: Jend the integral T the Substetution y= 2 seeo

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Q: b) Applying the concept of integration, find the total area between the x-axis and the curve: y =r -…

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Q: Use a double integral to find the area of the shaded region. 7/2 20 r= 9+9 cos e 10 - 10 -5 5 10 15…

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Q: y. x= y? – 2 y = 1 x= e" y =-1

A: Given the graph of a region

Q: Evaluate the integral by making an appropriate change of variables. 9 cos( 3 (Y-X)) dA where R is…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 17 – r…

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Q: Q1\ sketch the region of integration and write an equivalent double integral and evaluate the…

A: First we write the regions of given integration and the we draw a diagram. Next we apply the…

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ (3y - 7) dy/(y - 1)(y -…

A: Consider,

Q: Use a double integral to find the area of the shaded region. 1/2 10 r= 5+5 cos e -5 5 10 -10

A: The integral of a function is with respect to two different variables, so if f is a function of two…

Q: Use a double integral to find the area of the shaded region. 51n T/2 10 r = 5 + 5 cos 0 -5 5 10

A: We need to find area of the shaded region.

Q: Evaluate the double integral on the given region. Show the steps.    ∬ (6x^3+6y^2) dA; R: 4 ≤ x ≤ 6…

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Q: Evaluate the integral. V1-y² (x² + y²)dxdy

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Q: A/2 15 10 r=7+7 cos 0 -5 5 5 10 15 - 10 15

A: The graph of the curve is given by To evaluate: The area of the shaded region.

Q: Express the area of the following shaded region in terms of (a) one or more integrals with respect…

A: Area is a 2-dimensional quantity which is the measure of amount of space covered by a shape in the…

Q: Evaluate the integrals: (a)∫xex/2dx (b)∫e2xsinx dx. (c)∫xcos(2x)dx.

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Q: dA R: region bounded by y = 0, y = Jx, x = 4

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Q: The improper integral (A) e B) 0 с 00 D 1 8 0 edx

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→du=-dx=∫-e-x

Q: Which of the following integrals would yield the area of the region below? 2 x=y 3 1 0 x = 8y 00 8

A: A detailed solution is given below.

Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and…

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

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Q: Evaluate the integral. H (z(1 – 2z)*) dz =

A: topic - definite integral

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ y + 3/2y3 - 8y dy

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 5 Y2 = 2x + 30 %3D…

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