What is the area within the curve r? 16 cose? А) 30 В 28 C 26 D) 32

Q: Evaluate the following triple integral over half unit ball below y-plane(B), //| Væ² + y? + 2² dV. B

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Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

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Q: Find the area enclosed by the given parametric curve and the x-axis.

A: Given : Given parametric curve are x=t3+1 , y=2t-t2 We want to find the area enclosed by the given…

Q: The lateral surface area of a cone is changing at the rate of 6 cm2/sec, where S = tr Vr? + h². Let…

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Q: Find the surface area of the sphere with radius of 7 in. Leave your answer in terms of T. 287 in 2…

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Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

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Q: Evaluate the line integral, where C is the given curve. xevZ ds, C is the line segment from (0, 0,…

A: Consider the  line integral ∫Cxeyzds Where C is the line segment from (0,0,0) to (3,4,2).

Q: Calculate the integral Se , where C is the unit circle Select one: O a. 0 O b. - 2 ri O c. 2 mi d. -…

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Q: dr Let A be the area of a circle with radius r. If dt 5, dA when r = 1. dt find

A: A is area of circle of radius r A = πr2 Differentiate the equation with respect to t

Q: dr Let A be the area of a circle with radiusr. If dt dA = 5, find when r = 5. dt %3D

A: Here we use the application of derivative.

Q: Find the area enclosed by the given parametric curve and the y-axis. x = t – 2t, y = vt -

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Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: Find the area of the reglon that lies Inside both curves. r=V3 cos(0), r= Need Help? Watch It…

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Q: dr Let A be the area of a circle with radius r. If dt dA when r = 1. dt 3, find %3D %3D Question…

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Q: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

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Q: Evaluate the line integral, where C is the given curve. ds, C: x = t3, y = t, 0 sts 5 7814.5

A: Here we have to evaluate the line integral, where C is the given curve.

Q: Use the property: Je f(z)dz < ML where |f(z)|< M on the contour C, and L is the arc length of C to…

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Q: aluate the integral flR (1– -) dA where Ris the circle of radius 2 centered at the origin on the…

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Q: 93. which f the follouwing repreeents ene - dimenalional heat Sqeation? 46) du c2 au %3D (d)u + azu

A: Some definitions: Wave equation: ∂2u∂t2=c2∂2u∂x2 Where c∈ℝ is called wave speed. Laplace equation:…

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Let C be the unit circle oriented counterclockwise. A line integral that represents the area inside…

A: Use Greens theorem and Stokes theorem to solve the following question.

Q: let E E R : z = 2xy, 0 < x² + y? < 25 an area in R°. calculate the surface area of E. O(E)

A: Consider the given information. Sxyz∈R3:z=2xy,0≤x2+y2≤25 The surface area is defined as, Surface…

Q: Evaluate the line integral, where C is the given curve. Sc xy² ds, C is the right half of the circle…

A: Use parametric  method to solve

Q: dr Let A be the area of a circle with radius r. If dt dA when r = 1. dt 4, find

A: Solve the following

Q: Evaluate the cylindrical coordinate integral: L L dzr dr de O 647 O 87 O 167 O 1287

A: To solve the integral

Q: Evaluate the given contour integral, where C is unit circle z=1. 3e cosz 2z +4 -57 + 2z- 4i 3 z' +…

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Q: The inverse Laplace hransform F(s) = 31 + Inci2-s)-nc19-s) is of %3D

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Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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Q: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

Q: Find the area of the region enclosed by the curve r = 2+ cos (20). (1.) (3,( Bu Die Aya Yard 97…

A: To find the area of the region enclosed by the curve r=2+cos2θ

Q: Evaluate dV, where E lies between the spheres x + y² + z? = 16 and E x2 + y2 + z2 r + y + z 64 in…

A: Follow 2nd ,3rd step .

Q: Consider the inetgral (11z + 2) dA where Ris the region between the circles z? + y? = 9 and z2 + y?…

A: Since R is the region between the circles x2+y2=9 and x2+y2=100. Therefore, we describes the region…

Q: Let P be outside C(O,r) and S, T e C(0,r) so that PS and PT are tangent to C(0, r). Show that PS =…

A: Given that PS and PT are tangents. We know that the tangent to a circle makes a right angle with the…

Q: What is the area under the curve given the parametric equatio x = t3 and y = t° over [0,1]? O 1/8 O…

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Q: What is the differential for the total surface area of a frustum of a cone with i as the slant…

A: The formula for total surface area of the frustum of the cone with the given slant height l is Total…

Q: 3z3 + 2 dz =? Y (z – 1)(z² + 9) |z – 2| = 2 7.

A: We have to calculate the contour integral ∮3z2+2z−1z2+9dz, where circle is given by z−2=2. First…

Q: Let A be the area of a circle with radius r. If dA when r dt dr 4, find 4. dt

A: We have to find

Q: 15. Evaluate the contour integral e3z I (z+ 2)ªdz where C' is the circle |z| = . 9e6 2 O 27 9e-6 O…

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Q: e? dz, calculate give integral. When C is a circle z= 2 (z – 1)

A: Introduction :

Q: dr Let A be the area of a circle with radius r. If dt dA when r = 4. dt 2, find %3D

A: Consider the following formula: A=πr2 Differentiate above equation with respect to r: dAdr=2πr…

Q: Jind the Surface area of the part of the para boloid 2=X+y" lyrng Orer the regron R

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Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

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Q: Evaluate SR sin(r +y?) dA where R is the region bounded by the circles r+ y? =1 and r +y? = 4.

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Q: Compute the line integral Sy?a dl where y is the part of the circle centered at the origin and of…

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Q: Find the area of the surface z = x² + y? that lies below the plane z = 2.

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Q: Sketch the reglons enclosed by the glven curves. y = Vx, y= X= 16 y y 6 4 4 3 3 2 10 15 10 15 O-1…

A: Given : y = √x  y = 1/3 x  x = 16

Q: Let A be the area of a circle with radius r. If dA when r = 3. dt dr 3, find dt

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Q: Compute the area of the unit circle by computing the following double integral 1dædy. z² +y?<1

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