Instructions:- Write answer on the paper and upload PDF file in the Moodle. Do not write any answer in the box. Problem - 21: Determine the area bounded by the curves y = -z - 22z + 75 and y = (z – 3)°.

Q: Question 16 Find the area of the region bounded by the curve y2-4x and the lines x = 1 and x = 4.…

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Q: ermine the surface area generated when a portion of the curve in the 1st quadrant of = 9(x² – a²) is…

A: We have to find the surface area of region.

Q: solve the following problems. Draw the necessary figures for each. Find the surface area generated…

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Q: In  the given equation as  follows , find the area of the surface generated by revolving the curve…

A: Given: x=t ; y=4-2t; 0≤t≤2To find the area of the surface generated by revolving the curve about…

Q: The graph of y = x³ from (1, 1)to (5, 125) is revolved about the x-axis. Find the area of the…

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Q: A circle with radius 1 centered at (0, ) is tangent to two points of the parabola y = a². What is…

A: We have to find the area of the shaded region.

Q: Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. А. 4.3 В. 4.6 С. 4.9 D. 5.2

A: we have to find the length of the arc of the parabola x2=4y from x=-2 to x=2

Q: Use x = au, y = bv to show that the area of the ellipse x2 y? = 1 is rab. 62 a2

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Q: Graph the equations on a piece of a paper and shade the area of the region between the curves. If…

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Q: Question 7 Find the area enclosed by the curves y=2r², y=2x.x=- and x = 1 A) 45/51 B 65/89 59/76 D)…

A: Here is the solution

Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

Q: x² : 4ay from x 0 to x = 2a

A: We have to compute the surface area of revolution of the curve x2=4ay about the y-axis between the…

Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

A: Given   Area of surface area revolved about x axis formula is

Q: Find betwee y = x2 the the CurveS and area 2. 3= 4x-x groph %3D Draw

A: Given curves :

Q: Question 2: Find the surface area of the object by rotating y = 4 + 3x2,1<x<2 about the у-аxis.

A: To find the surface area of the object by rotating y=4+3x2, 1≤x≤2 about the y- axis. Since the…

Q: B Fig 1 1 y = (3x)3 A I. Find the co-ordinates of A and B X II. Find the area enclosed by the curves…

A: Please see the below picture for detailed solution.

Q: Q2. An object is kept at a distance of 20 cm from a concave mirror. A real mage is formed at 20 cm…

A: Topic:- algebra

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y=x3 + for…

A: surface area of the curve is given by  S=2π∫abf(x) (f'(x))^2+1 dx

Q: Question 7 Find the area enclosed by the curves y=2r², y=2\/x,x=- and x = 1 A 45/51 B 59/76 49/96…

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Q: Question 2: Find the surface area of the object by rotating y = 4 + 3x²,1 < x < 2 about the У-аxis.

A: y=4+3x2,  1≤x≤2 Now differentiating y=4+3x2 with respect to x, we get dydx=0+32x=6x

Q: Graph the equations and shade the area of the region between the curves. y = 20 − x, y = sqrtx, and…

A: The region is bounded by the curves y=20-x, y=x,y=1

Q: Question 2: Find the surface area of the object by rotating y = 4 + 3x²,1 s x s 2 about the у-аxis.

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Q: Question 12 Calculate the area of the smaller region (to the left of the parabola) bounded by…

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Q: The ceiling of a building has a height above the floor given by z = 30 + x, and one of the walls…

A: The surface area can be given by SA=∫abf(x)ds =∫040(30+14x)ds Path is given by…

Q: 5. Consider the shaded region shown in the figure that involves the curves of equations: (x – 1)? =…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

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Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

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Q: 9y=x²,0 ≤ x ≤ 2 ; x-axis

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Q: stuck on the attached problem

A: Please refer to the white board. We have to find the volume shaded in the first diagram. This volume…

Q: 1 x = + 6 2y What is the length br of the portion of the graph of the between the points with y = 1,…

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Q: The diagram shows part of the curve y? = x+1 which intersects the axes at A and B. The area of the…

A: given,

Q: Find the area of the sector associated with a single slice of pizza if the entire pizza has a…

A: Given: Create a problem for arc length degree measures between 15 degrees and 345 degrees. To find…

Q: Question 18 Find the area bounded by the curve y 8 square units 4 square units 16 square units 10…

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Q: QUESTION 13 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+…

A:

Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

A:

Q: QUESTION 14 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: We need to find area.

Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

Q: () X+Cy-1)=1 of the circle y=-l calkulate 2. the area of the surface formed by rotating it around…

A: Given equation of circle:   X² + (y-1) ² = 1 Equation of line:   y= -1

Q: Any help will be useful.

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Q: Consider a closcd rectangular box with a square base with side æ and height y. a. Find an equation…

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Q: (i) On the same diagram, sketch the eurves y? =-* and y x (ii) Find the exact r-coordinate of the…

A: The solution is given below in the next step:

Q: Question 7 Find the area enclosed by the curves y=2x², y=2√x,x= — and x = 1 A 45/51 B) 59/76 49/96…

A:

Q: Question 8 Given the equations x = y2,y = I Find the area and volume bounded by these curves if the…

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Q: The figure below is a plot of the equation of the line y = A/x where A = 7.2.  Determine the surface…

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Q: Find the area of the curve r2 = a2cos2θ and provide a correct and accurate graph for the curve…

A: Find the area of the curve r2=a2 cos2θ

Q: 13. Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y,…

A:

Q: QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: Please see the below picture for detailed solution.

Q: A point moves on a curvilinear path with equation (S = t + 5t). the total accelera on is (8.39) m/s…

A: total acceleration =sqrt[(tangential acceleration)^2+(radial acceleration)^2]

Q: Find a formula for the area of the ellipse a2 y? =1 (where a,b>0). 62 Show and explain ALL your work…

A: lets the area A = 4∫0aydx lets write x = asin(t)   y = bsin(t) dx = acos(t)dt limit is o to π/2 A =…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.