Exercise 5 Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the curve x = 2Vy, above left by the curve x = (y – 1, and above right by the line x = 3 - y. x= (y – 1) = 3 - y ol

Q: The area bounded by the curve x = 5y + 7, the y-axis and the abscissas y = 0 and y = 2 i . %3D 12 19…

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Q: find the area of the region bounded above by the curve y = 2e^-x + x, below by the curve y = e^x/2,…

A: To find the area of the region bounded above by the curve y=2e-x+x, below by the curve y=ex2 on the…

Q: Q-1- Find the area of the region bouncledby the Curve y= xe and the XaaXis froam X=o to x = 4 ?

A: To find the area of the region bounded by the curves

Q: Q:: Find the area bounded by the curve Vx+/y = 1 and the coordinate %3D axes, at x = 0,and y = 0

A: lets assume a horizontal strip under the region boundedwe get0≤x≤(1-y)2 0≤y≤1

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: We will first sketch the curve and the line.

Q: Find the area of the figure bounded by the curve a) y = 1+/# » Y = 0 x = 1 1+va y = b) x = 4 cos t y…

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Q: Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: || xydA where R is the region bounded between the curves y = e²-1, y = e'¬², and x = 0. R.

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Q: Find the area enclosed by the x-axis  and the curve x = 1 + et y=  t - t 2

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Q: 1. (a.) Find the area bounded by the two curves; y=r+x-10 and y=-+Sx+6. i y=r-3r and y = 2-x

A: i) Given curves are, y=x2+x-10 & y=-x2+5x+6 Let's draw table for y=x2+x-10 x 0 1 2 4 y -10…

Q: The x-coordinate of the centroid of the area in the first quadrant, bounded by the curve y=x², the…

A: X coordinate of the centroid

Q: A) the curve of f(x) Use the picture to evaluate the area under y=fx) a) | f(x)dx (b) 1 4. 6. c)

A: To find the following areas from figure

Q: ind the centroid of the region bounded by the graphs of the functions y = 6a?, y = x² + 7 The…

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Q: Find the area enclosed by the curve x= t2-2t, y = √t and the y-axis.

A: The area enclosed by the curve x=t2-2t, y=t and the y-axis

Q: Find the area enclosed by the x-axis and the curve y=1tet v=t-t2. (Show all work separately and…

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Q: %3D Ex 4: -Find the area bouinded by the curve y = x² and the line y = x.

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Q: 5. Find the centroid of the area bounded by the curve y = 4- x², the line x = 1 and the coordinate…

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Q: Find the area enclosed by the given curves a) y=x^3, y=-x, x=-1, x=1 b) y=x, y= -1/x, x=1/e, x=e

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Q: Find the area between the curve y = x(x-1)².y = 2 and the y-axis a.) 5 sq.units 25 b.) 4 sq. units…

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Q: a) Sketch the curve and find the total area between the curve and the given interval on X-axis. i) y…

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Q: f the region enclosed by the Curve y= Sin (Tx/2) and the tind the area line

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Q: Find the area enclosed by the curve x = t2 - 4t, y = -Vt and the y-axis. A = S rdy or A= S. (TR-IL)…

A: x=t2-4t, y=-ty=0 →t=0y=-2 →t=40≤t≤4dydt=-12t

Q: Find the area under the curve y 12 over the interval [ – 1, 1]. %3D (x + 2)² area = i

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Q: ind the area bounded by the given curves. 1.) 2x+1, x+y=7, x=8 2.) y^3=x^2, x-y=2, x+y=2

A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: Find the area bounded by the ff. curves and lines: a. the loop of y^2 = x^4 (5 - x) b. x^2 - y^2=…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: y = x y = 1 1 y = →x 1 b. 2.

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Q: 6. Find the number a such that the line x = a bisects the area under the curve y = 1 1<I< 4.

A: The given data is: Find the number a such that the line x=a bisects the area under the curve:…

Q: Find the area under the curve y = 18 - over the interval [ – 1, 1]. %3D (x + 2)? area = i

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Q: 2. у? -8х- 8y +8%3D0 a. Find the area bounded by this curve and its latus rectum

A: 4px-h=y-k2 is the standard equation for a right-left facing parabola with vertex at h,k and focal…

Q: -ind the total area bounded by the curves y== x° - 4x and y= x+2x

A: If the two curves f(x) and g(x) are given then the total area bounded by these two curves can be…

Q: Find the area under the curve y 24 over the interval [ – 1, 1]. (x + 2)? area = i

A: By Solving area under curve

Q: 2. Find the centroid of the area in the first quadrant under the curve y = 4 – x2. Answer:

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Q: Jx and y = x Q No. 5 Find the area bounded by the curves y =

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Q: I+y = 0, x = y2 +3g

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Q: Activity 2. Find the surface area generated by the following by rotating at the given axis 4. f(x) =…

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Q: Find the area bounded by the curve xy = 2 and the line x+y = 3. A. 0.17 sq. units B. 0.11 sq. units…

A: Given problem:- Find the area bounded by the curve xy = 2 and the line x+y= 3

Q: IV. Find the area bounded by the given curves; 1 y= , y=0, x=1, x = - 1. 1+x? Sketch the curve…

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Q: Find the area bounded by the curve xy 2 and the line x+y%3D 3. A. 0.17 sq. units B. 0.11 sq. units…

A: Let's find.

Q: Find the area enclosed by the y-axis and the curve x = t – t²,y = 1 + e¬t.

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Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: 34. Find the area enclosed by the curve x = t2 – 2t, y = Vi and the y-axis.

A: Given

Q: a) Sketch the curve and find the total area between the curve and the given interval on X- аxis. i)…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 5. Find the area bounded by the curve y e, x- axis and y- axis. С 2 A 0 В 1 D Infinity

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Q: Find the area of the region bounded by the given curves. y = 1/x, y = x2, y = 0, x = e

A: Given curves, y=1x, y=x2, y=0 x=e

Q: Calculate the total area of the curve y=x' and the x-axis between x-2 and x=-2. O 8 sq units 11 sq…

A: The given bound region is: Now taking vertical elementary strip; So, the area of the strip from the…

Q: Find the area enclosed between the X-axis and the curve y = (x +1)°,0 < a < 3.

A: The area under a curve is the area between a curve fx and the x-axis on an interval a, b given…

Q: IV. Find the area bounded by the given curves; 1 y= v?' y=0, x=1, x = - 1. 1+x? Sketch the curve…

A: Let's find.

Q: Find the area bounded by the curve y = x + 3 and y = x²+x-13, from x=1 tox=3. a. 23 sq. units b. 20…

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Q: Find the area under the curve y² = x and y = x² 1 a.) sq.units b.) = sq.units c.) 1 sq.units 2 d.)…

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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.