1a)Evaluate the double integral over the rectangular region R: ∫∫R 4xy^3 dA;R=(x,y) :−10≤ x ≤10,−8 ≤ y ≤ 8

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: 8) Evaluate dA, R: 1st quadrant bounded by y² = x & x² = y R 9) Evaluate ff sin (y) dA, R: the…

A: As per our guidelines we are supposed to answer only first question.kindly repost other parts. Thank…

Q: sketch the region bounded by the given lines and curves. Then express the regions area as an…

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Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Determine the area of the region bounded by CTTY), x- 3, y=O,& y=4

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Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

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Q: Q2) find the area of region in second quadrant within cardioid r =1-cose

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Q: Q1) Sketch the region enclosed by the curves and finds its area y=sin2x y=0, x=, x 4

A: The objective is to find the area of the region enclosed by the curves y=sin2x, y=0, x=π4, x=π2 The…

Q: y=x² (-2,4) 0 (1,6) (2,4) 3y = 2x + 16 y=-2x+8 X

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Q: 5) Consider the parallelogram with vertices (0,0), (4,0), (6,2) & (2, 2). We know the area of this…

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Q: Find the area bounded by the region y = 2x + 2 and the lines y = 1, y = 2

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Q: Find the area of the region bounded by one loop of the curve y"(1 - у?)

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Q: Find the area of the region bounded by y²= 8x and y=x With figure and representation

A: Given,y=x...............(1)andy2=8x..................(2)on solving equation (1) and…

Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

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Q: 4. Find the area bounded by the curve (x+y)^5 = ax^2y^2 in the 1st quadrant, where a is a constant.…

A: Let x=rcos2θ, y=rsin2θ L.H.S: x+y5  rcos2θ+rsin2θ5=rcos2θ+sin2θ5                          =r5…

Q: Write a line integral(s) that would give you the area the graph of f(x,y)=x^2-3y^2-4x+6y+30 and the…

A: The line integral of  function F along with curve C is defined as  ∫CF·dr=∫C(M,N)·(dx,dy)=∫CM dx+ N…

Q: Evaluate ∫∫R sin(x^2 + y^2) dxdy where R is the region inside the circle x^2 + y^2 = π.

A: Given the function f(x,y)=sinx2+y2 Note that the given region R is the circle x2+y2=π with a center…

Q: 3) Let R be the region in Q1 bounded by the graphs of these equations: y =16-x²,y=-4x+16 Sketch R on…

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Q: Find the area of the region bounded by y = x2 + 2x - 1, y =+x- , x = -3, x = 1.

A: As per our guidelines, we are supposed to solve only one question. Kindly repost other question as…