4. Evaluate dA, where D is the region in the first quadrant enclosed by y = x², y = 5, D V1+y? and x = 0.

Q: Evaluate O y°dx – x°dy, where C is the boundary of the region between the circles x? + y? = 25 and…

A: In the question we have to find the region between given circles.

Q: 2) Evaluate JJ (x – 1)dA; for the region in the first quadrant enclosed by y = | x³, y = x.

A: Given that, ∬(x-1) dA ; for the region in the first quadrant enclosed by y = x3,  y = x. First, draw…

Q: Evaluate the integral (2.x - y)dA, where D is the region in the first quadrant enclosed by the lines…

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Q: If R is the region æ² + y² < 4, then Sp(æ² + y³ ) dA = S* L r² dr d0. 2

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Q: By switching to a suitable set of coordinates, calculate the area {(x, y) E R² : 2y² < x < 3y², 1/x…

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Q: b. [[(x? + y2)dA; Ris the region bounded by y = x and y? = 4x.

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Q: 3. Find the area of the region in the first quadrant that is bounded by y=Vx , x-axis and y=x-2. |

A: 3) To find the area under the curve in first Quadrant

Q: 2- SS, xy dA {(r, 0)|0 <r < 1, | and the region in the first quadrant }

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Q: Find the area of the shaded region. y y = Vx 3 마1, 1) x = 27 1 y = X 5 10 15 25 20 2.

A: The area under the graph can be determined by integration. Let, Boundary points are, x1=1 and…

Q: By making a suitable change of variables, evaluate y SS, = dx dy where A is the region in the first…

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Q: Evaluate ([7y'e*+ dA where D is the region bounded by y = 2 x , x=9 and the x-axis.

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Q: Give area of the region enclosed by y and y = 0 from x = 1 to x = 3. 2 A. 2 В. 3.4 С. 1.5 D. 1

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Q: Consider the following shaded region. YA y=ax - x? y=bx Find the area S of this region if a = 4, b =…

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Q: 3. Evaluate -dA where D is the region in the 1" quadrant bounded by y =x' and y= 4x.

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Q: 3. Evaluate ff x²dA; for the region in the first quadrant enclosed by xy = 1, y = x,y = 2x.

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Q: d) Find the volume of the solid formed when the area bounded by the curve y = 3x – x? and the lines…

A: The volume of the solid generated by the revolution of the area bounded by the curve y=f(x), x-axis…

Q: Give area of the region enclosed by y and y = 0 from x = 1 to x = 3 2 А. 2 В. 3.4 С. 1.5 D. 1

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Q: Find the area of the shaded region.

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Q: 49. SR 3xy dA; R is the region in the first quadrant bounded by y = 2 x, y = 0, and x = 4 − y². =

A: Given Region  is bounded by  curve y=2-x, y=0 , and x=4-y2  in first quadrant

Q: Calculate ∫∫(x^2 + y^2)^3 dA. Where D is the region in the first quadrant                  D…

A: Concept Used:- In polar coordinates x=r cosθy=r sinθ ⇒x2+y2=r2 Consider the region D bounded by y=x,…

Q: Evaluate y°dx – x°dy, where C is the boundary of the region between the circles ? + y = 4 and x2 +…

A: Consider the given integral. I=∮Cy3dx-x3dy  And, the regions are x2+y2=4 and x2+y2=16. The green…

Q: 3. Evaluate sse- Ne-cx)) JA where D isthe region shown below ニxく ソュ -x

A: The given integral is,∫∫D(3-6xy) dA

Q: D. Find the area of the region bounded by the given curves. Breaking 1 NEWS x2 = 4y 3 y? = 4x %3D 2.

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Q: 1. If R is the region in the first quadrant bounded by x-axis, 3x + y = 6 and y evaluate 3x, Jf 3y…

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Q: . A factory that makes smartphones z is thousands of phones, and a m the area of the region above…

A: Given: Marginal cost of smart phones, numbers of phones, marginal revenue function. To find: Area of…

Q: Find the area enclosed by the given curves. y = x°, y = 4x 4. O 16 2 8.

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Q: 22 Evaluate f, e-(x²+y?) dx dy, where R is the region x? + y? < a?.

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Q: Find the area of the shaded region. y y= 9 x – x² 15 (7, 14) 10 5 y= 2 x 2 4 6. 10 CO 20

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Q: Evaluate 1 dA x² + y² +1 where R is region in the first quadrant bounded by y = 0, y = x and x² + y²…

A: We have to evaluate ∬1x2+y2+1dA The region R is in the first quadrant bounded by y=0, y=x and…

Q: Evaluate C, dxdy, by first reversing the order. . Se ye" x' i) Draw the region R for the above…

A: This question is related to Integral calculus

Q: Evaluate (x – 3)dA where Ris the region in the first quadrant enclosed between y = x and y = x'. R…

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Q: Evaluate // xye-(x-+y") dA where D is the region between the two circles x2 + y² = 1 and x2 + y² = 9…

A: Consider the given integral, The region D is a bounded region between the circle of radius 1 and 3.…

Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

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Q: Sketch the region enclosed by the given curves. X = = 8y?, x = 4 + 7y2 y y 30 30 25 25

A: Given equations x=8y2x=4+7y2 Graph both the equations using graphing calculator

Q: Find SS, (x2 + y²)dA, where D is bounded by y? = 4x and y = x.

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Q: Approximate the area of the shaded region using the Trapezoidal Rule and Simpson's Rule with n = 8.…

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Q: Evaluate (x – 13)dA where Ris the region in the first quadrant enclosed between y = x and y = x'.

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Q: Evaluate (x – 2)dA where Ris the region in the first quadrant enclosed between y = x and y = = x³.

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Q: Find the area of the region R enclosed bg the parabala y=x² and the line y=X+2.

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Q: If R is the region in the first quadrant bounded by x-axis, y = x 2 and 2x + y = 3, evaluate ZZ R x…

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Q: Let R be the region given by 0 SzS a? + y? , a² + y? <3. Evaluate (x + 2)dV.

A: The given integral is ∭Rx+2dV where R is the region given by 0≤z≤x2+y2, x2+y2≤3. We know that the…

Q: Evaluate O y*dx – x* dy, where C is the boundary of the region between the circles x² + y² 1 and x?…

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Q: If R is the region in the first quadrant bounded by r-axis, y = }a² and a + 2y = 2, evaluate 1. a…

A: In this question , Firstly we can draw the given region R and find where the 'x' and 'y' limits vary…

Q: Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and…

A: Area bounded by the curve y=x2 and the line y=2-x

Q: 10) Find ff, (x + y) dA where R is the region in the first quadrant bounded by x2 + y2 = 4, y = x…

A: x2+y2= 4 is a eqn of a circle having center at (0, 0) and radius is 4y = x is the eqn of a straight…

Q: Describe in words the region in R’ represente + z? > 4 he equation x + y²

A: Here we have to describe the region in R3 represented by the equation x2+y2+z2≥4

Q: Evaluate y°dx – a*dy, where C' is the boundary of the region between the circles a + y = 4 and a + y…

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