iv. Sketch the region of the following iterated integral then evaluate it ex²+y² dy dx.

Q: Use an iterated integral to find the area of the region. dy dx = y 6r 5- 3 2 1 -1 1 4 6 3. 2. 4.

A: Given:         From the above graph :               We can say that the function is y=x        Area…

Q: Use an iterated integral to find the area of the region. dy dx = y 8 7 5 4 3 2 1 -1 1 4 -1l 3. 2.

A: We need to setup and evaluate integral.

Q: Use an iterated integral to find the area of the region. y = 4 - x2 dy dx = y 5- 3 2 1 -1 1 3 -1F 2)

A: The equation of the curves bounding the region are C1: y = 4-x2C2: x = 0C3: x = 2 To evaluate: The…

Q: Sketch the region R whose area is given by the iterated integral. 7-y dx dy ly/6

A:

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x² dy = ƏN aM dA əx for the given path.…

A:

Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

A: We first sketch the region using a graphing calculator.

Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy = Ne dA ду for the given path. C:…

A: Greens  theorem verification

Q: Use an iterated integral to find the area of the region. y = 25 - x2 dy dx = y 25 20 15 10 5 1 1 2

A: The equation of the curve is given by y = 25-x2 The graph of the region is  To evaluate: The area…

Q: The double integral J 2xy dA over the rectangular region R= {(x, y) E R, 0<x<4 and - 1<y<0} is equal…

A: Consider the given integration as ∬2xy3dA And given limit as 0≤x≤4 and -1≤y≤0

Q: Verify Green's Theorem by evaluating both integrals ƏM ? dx + x² dy dA ax ду for the given path. C:…

A: Given : ∫c y2 dx + x2 dy , Where, c : boundary of the region lying between the graphs of y =x &amp;…

Q: Evaluate the triple integral I = y dV where D is the region in the first octant (x > 0, y > 0, z >…

A:

Q: Calculate the iterated integral 5-x dx dy 2 х —1 and draw the region over which we are integrating.

A: To evaluate: ∫23dx∫x-15-x1ydy

Q: Sketch the region of the following iterated integral then evaluate it CV1-x² L, -* e**+y* dy dx.

A:

Q: Evaluate the double integral || x sin(xy)dA over the region R={(x, y)| 0<x<,0< y<1}. 4

A:

Q: Use an iterated integral to find the area of the region. 1 y = Vx - 7' 8 < x< 32 dy dx = y 2.0| 1.5…

A: Given, x is viaries as  8≤x≤32 And from the Graph y varies from 0 to y=1/√(x-7)

Q: Verify Green's Theorem by evaluating both integrals aM dA ƏN | y? dx + x2 dy = ду, дх for the given…

A:

Q: Use an iterated integral to find the area of the region. y = 64 – x2 dy dx = y 60 50 40 30 20 10

A: From the given figure, Now find the x-intercept and y-intercept; x-intercept:…

Q: Evaluate the integral of the two-form w = (x8 + 2y) dx A dy over the region D bounded by the curves…

A:

Q: Verify Green's Theorem by evaluating both integrals ƏN y2 dx + x² dy dA ay for the given path. C:…

A:

Q: Evaluate the double integral / |: xy dA where D is the region bounded by the line y = x – 1 and the…

A:

Q: The double integral ff 2xycosydA over the rectangular region R = {(x, y) E R?, 0< x<1 and 0 <y<n}is…

A:

Q: 1. Sketch the region and evaluate the following integral |1. (VI++1)dydx 72 y 4 2 ++++++++H 3 -1 1 4…

A:

Q: Evaluate the integral. JS 2x + y dA D where D is the region bounded by y=x, y=0, x=2.

A:

Q: Sketch the region R whose area is given by the iterated integral. dy dx

A:

Q: Sketch the region R and evaluate the iterated integral | f(x, y) dA. 30 15 (x + y) dx dy Jy/2

A:

Q: Use an iterated integral to find the area of the region. dy dx = y 10 9 8. 7 6 5 4 3 2 1

A: As we know that; The equation of the line when it passes through the points x1,y1 &amp; x2,y2…

Q: Sketch the region R and evaluate the iterated integral ffa (12x+4y) dy dx Ја Јахо f(x, y) dA.

A:

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy = dA ду ax for the given path. C:…

A:

Q: 1. Let A be the region enclosed by the curves y = r² + 1, y = (2x – 1)² and r = 1. 2 ty y = x² +1…

A:

Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

A:

Q: Verify Green's Theorem by evaluating both integrals aN y2 dx + x2 dy dA ду - əx for the given path.…

A: For c-1 sign is negative because of opposite direction

Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

A:

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

A: Given data: The given integral is ∫∫Rx1+y2-1/2dA. The first function given is y=x2. The second…

Q: State Green's Theorem and hence verify the same for the integral [{(x- y)dx + 3xydy} where C is the…

A:

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy dA ax ду for the given path. C:…

A:

Q: Verify Green's Theorem by evaluating both integrals | y² dx + x2 dy dA ax for the given path. C:…

A:

Q: Verify Green's Theorem by evaluating both integrals dA v? dx + x2 dy ax for the given path. C:…

A: We have to verify the green's theorem

Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

A:

Q: Sketch the region R and evaluate the iterated integral f(x, y) dA. 30 15 (x + y) dx dy 16 30 14

A: We have to sketch the region and evaluate the integral:

Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

A:

Q: Use an iterated integral to find the area of the region. dy dx = y 6 5 4 3 2 1F -1 1 2 4

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Use an iterated integral to find the area of the region. 4 dy dx = 16 y 5 4 2 1 1 3 4 6 3.

A: This question is related to double integral , We will solve it using given information.

Q: Use an iterated integral to find the area of the region. y = 4 – x2 dy dx = y 5| 3 2 -1 1 3 -1}

A: Given,              y = 4-x²

Q: Verify Green's Theorem by evaluating both integrals aN | y2 dx + x² dy dA ax for the given path. C:…

A:

Q: Ise an iterated integral to find the area of the region. dy dx = Jo y 8 7 6 5 3 2 -1 4 7. 8

A: We want to find area shaded in diagram.

Q: Verify Green's Theorem by evaluating both integrals an_ am | v² dx + x² dy = dA ây for the given…

A:

Q: Use an iterated integral to find the area of the region. 5 sxs 40 dy dx = !! y 2.아 1.5 1.0 0.5 10 20…

A: