1. Find the area of the given region bounded by the graphs of y, = x² + 2, y2 = 4 – x², and y3 = 2 – x, as shown in the figure below. | y2 -1 3.

Q: Below is the graph of y= r +5. 20] 15 10 -2 -1 0 1 4 The area bounded by y= z+5 and the zaxis from…

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Q: Q1. Find the area of the bounded region shown in Fig 1. [8] y = x 2 y = \x+2 -2 2 Fig 1

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Q: Consider the region bounded by the graphs of y = x2 and y = b, where b > 0. Sketch a graph of the…

A: The given graphs are y=x2 and y=b, where b>0 we have to sketch the region bounded by the graphs…

Q: 11. Find the area of the region bounded byy = (x - 1)² + 1, the x -axis, x = -1, and x = 2. A. -6 C.…

A: Here we are using integration method to find the area of the given region.

Q: 4. Find the area of the region bounded by the graphs of f (x) = x³ +x2 – 6x and g(x) = 2x – x2 20 А.…

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Q: et l2 be the same region as in part (2). Write this region in the form 12 = {(z, y) : e<ysd: a(y)…

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Q: 14 12

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Q: Find the area of the region bounded by the graph ofy =1/x the x-axis, and the vertical lines x = 1…

A: The area is calculated by taking a rectangular element of width  dx and height y. The total area is…

Q: 41. S = {(x, y) |x> 1, 0< y sey 41-46 Sketch the region and find its area (if the area is finite).

A: The given region is: S= (x, y)| x≥1,  0≤y≤e-x

Q: 1. Find the area of the region bounded by y = 4 – x², y = x + 2, x = -2, and x = 1.

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Q: Find the area of the region. f(x) = (x – 5)3 %3D g(x) = x – 5 y 1.5F 1.0 0.5 1 2 4 /5 6. -0.5 -1.0…

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Q: 1 10. Rotate the region bounded by y=y=9, x = -2, x = 3 about the x-axis.

A: Note: Volume V of revolution about the x-axis is given by V=∫abπ y2dx .

Q: Find the area of the given region bounded by the graphs of y1, y2, and y3, as shown. y1 = x2 + 2, y2…

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Q: Let R be the region below bounded by the graphs of C1: x2 + y2 = 16, C2: y = 4 − (x + 2)2, and C3: y…

A: Given,C1 : x2 +y2 =16 , C2 : 4-(x+2)2, and C3 : -4x-4 To find the arc length of the portion C2 , the…

Q: In the given question , find the area of the region bounded by the graphs of the equations. y = -x2…

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Q: 1. Find the area of the region bounded by the boundary conditions below: (complete with graph) a. y…

A: We have y=x+5 , y2=x , y=2, y=-1 Now, the region can be graphed as below: The area lies from y=-1…

Q: If F =, and C is the boundary of the region bounded by the curves y =x, y=x´ in the first quadrant.…

A: Given F→=3xy2,10cosy. To evaluate ∫CF⇀.dr→, where C is the region bounded by the curves y=x and…

Q: Consider the following equations. 124 O Sketch the region bounded by the graphs of the equations. y…

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Q: In finding the area between the regions y = x2 – 2x and y = - x, the limit values of x are О а. 1, 1…

A: The given curves are y=x2-2x and y=-x.

Q: Which of the following represents the area of the region bounded between the graphs of y= x² + 3x…

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Q: 2. Evaluate |(xy)dA over the region R=[4,7]x[4,6] R.

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Q: If R in the formula f, dA is the region bounded by x = y and x =y, find the area of region with…

A: Double integration problem...

Q: 1. Find the area of the region bounded by y = -4x + 9, y = 2x² – 11x + 9, and the lines r = -2 and a…

A: It is given that, y=-4x+9y=(2x2-11x+9)   Area under the region can be calculated by using the…

Q: 9. a) Find the area of the region bounded by the y = Vx and y = x 1 graphs of (set both equal and…

A: To find the area of the region bounded by the curve and a line , find the intersection of both and…

Q: 12.) Find the area of the given region analytically. Between the loops of r = 1+ 2cos®

A: Area of the polar curve, r is given by:

Q: Find the area of the region bounded by the graph of a.) x = y² - 4 and x - 2y =1 b.) y = 9 - x²…

A: (a) Given: x=y2-4……1x-2y=1……2

Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y b) x = y¹,…

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Q: 3. Find the area of the region bounded by the graphs of y = 2 - x² and y = -x. 4.5 O 1.5 O -1.833…

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Q: Which of the following gives the area of the region between the graphs of y =x3 and y = -x from x= 0…

A: Given, y=x3,y=-xfrom x=0 to x=2

Q: Sketch out the region {z E C : Im(z²) > 0, 1 < |z| < 2}.

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Q: A region bounded by f(x) = x² + 1, y = 1, and x = 2 is shown below.

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Q: Find the area of the region bounded by the graph of f(y) = y2 and the y-axis for 0 ≤ y ≤ 1, as shown…

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Q: Find the maximum and minimum of w(x, z) = 2xz + z^2 +1 in a region R bounded by x = 0, z = 0, and x…

A: The bounded region R is:

Q: 9-1. Find the total area of the regions enclosed by the given curves: (a) x = y2 and x = y+2 (d) y =…

A: First find out the intersection points of both the curves than integrate in that interval with…

Q: *** Which of the following represents the area of the region bounded by y= x+2 and y= x2 ?

A: Area is bouded by curve y=x+2  and y=x2

Q: 17. Sketch the region and find its area (if the area is finite): S = {(x, y) | x 2 1, 0<yse2}

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Q: Let f (x) = x³ + 5x and g(x) = 7x2 - x %3D %3D Determine the area A of the region enclosed by the…

A: TO FIND THE AREA ENCLOSED BY THE GIVEN FIGURES .FIRST FIND THE INTERSECTING POINTS OF THE CURVE BY…

Q: Find the area of the region bounded above by y = -x2-3x-2 and below by y = -2. AY 51 4 3 54 32 t 1 2…

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Q: Below is the graph of y = a2 +5. 14 12 10 8- 6- 4- 2- -3 -2 -1 1 2 The area bounded by y = x2 +5 and…

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Q: 2. Use a geometric formula to determine the area of the region given by f: V25 – x5dx. -5

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Q: Which of the following gives the area of the region between the graphs of y =x5 and y = x from x= 0…

A: Graph of given curves will be

Q: Below is the graph of y = z2 +5. 301 2어 1어 -4 -3 -2 -1 0 i 2 3 4 5 The area bounded by y = z2 +5 and…

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Q: 7.5x A sketch of the region enclosed by y = x and y follows. x2 + 1 -3 -2 -3 Area of the region =

A: Let's find.

Q: Find the are of the region bounded by the graphs of the given equations f(1) = 5x² and h(x) =r² + 1.

A: To find: The area of the region bounded by curve fx=5x2 and hx=x2+1. Formula used: The area of the…

Q: 4. Evaluate 15x-6ydA where D is the region bounded by x=ty and x=

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the area of the given region bounded by the graphs of y1, y2, and y3, as shown. y1 = x2 + 2, y2…

A: Given that, y1=x2+2y2=4-x2y3=2-x We have to find the area of the region bounded by the above…

Q: Which of the following gives the area of the region between the graphs of y =x2 and y = -x from x= 0…

A: We have to use area between the curve formula.

Q: О к The area of the bounded region below is ec x2 C X²

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.