1. Find the total area bounded by the curves y = sin (x), y = cos (x), x = 0, x = n. Graph curves.

Q: 2. FIND THE AREA BOUNIDE O BY 2 y= x (2,4) and the X- axis THE CURVE

A: The given curve is: y=x2      .........(1)We have to find the area bounded by the curve y=x2, (2,4)…

Q: 1. Calculate the area of the graph enclosed by the curve y = sec(2x)tan (2x), the x-axis, and the…

A: The given curves are y=sec2xtan2x, x=0, x=0.5, y=0 To find the area of the region bounded by the…

Q: 4. a. Draw a region R bounded by the curves y = x² +4 and y=x+2, then detemine its area. b. Find the…

A: We have to draw the region R bounded by the given curves. Then, we have to find the area, and then…

Q: 1. Find the first quadrant area bounded by the curves 20 y = 4+x2 y = 1 and x = 0

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Q: What is the area between the two curves specified from x = 0 to x = 1? A numerical answer alone is…

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Q: 1. Find the area of the region enclosed by the given curves. y = cos x, y = 2 – cos x, 0 < x <T

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Q: Find the area between the following curves. x= -3, x= 1, y=e^, and y-3- e 2 (Type an exact answer in…

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Q: 5 for 0<x < 7. %3D Calculate the area of the segment between the curves y = sin x and y =

A: To find the area between the curve

Q: 9. (a) Calculate the area of the region bounded by the curves y = x² +1 and y = xª between x = 0 and…

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Q: 1.Find the area bounded by y=sin(sin x), the X- and x = π axis and the lines x = 0

A: See this solution in below.

Q: 4. Find the area of the region that lies inside the curve r = 1 – sin 0 and outside the curve r = 1.

A: It is required to find the area of the region that lies inside the curve r=1-sinθ and outside the…

Q: 1 Find the area onclosed by the Curve r=4-3 sin 0.

A: Area

Q: Find a formula for the area A(w) of the triangle bounded by the tangent line to the graph of y = In…

A:

Q: 1. Find the area between the curves of y = x2 +1 and y = x +7 from x = -2 to x = 3. Round to two…

A: Topic-application of integration

Q: 4. a) calculate the area of the area bounded by the Curves TI y=Sin 2x and y sin 2x, OSX<

A:

Q: Find the area between the curve y = tan x and the x-axis from x = -pai/4 to x = pai/3.

A: Given information

Q: 2. Find the total area of the region between the curves y = sinx and y = cosx for 0<xs 37 2

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Q: Area between curves y=e^5x y=e^3x x=1

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Q: Question 4. Find the area bounded by the indicated curves. y =x- 9x, y = 0

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Q: 4. Set up the integral for the area of the surface obtained by rotating the curve y = e-x -1 < x< 1.…

A: Given: The area of the surface obtained by rotating the curve y=e-x2  and -1≤x≤1 we have to…

Q: 1) Find the area of the region bounded by the curves: x=2y2 and x=16+y2 2) Find the area of the…

A: Important points: 1. First we will draw both the parabolas by finding their vertex. 2. Then we will…

Q: Find the area enclosed by the given curves. TU TU 26) y = sin x, y = csc 2 x, ≤x≤ 3 2 27) Find the…

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Q: Find the area of the region enclosed between y = 3 sin(x) and y = 2 cos(x) from x = 0 tox = 0.5x.…

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Q: 17 1. Find the area between the curves y=- 9+x 13 and y=- 1+x

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

A: This is a problem related to calculating area under curve of the polar equation. Based on the…

Q: Question 3: Find the area between the curve y = 4 – x² and the line y = -x + 2.

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Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

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Q: 1)Find the area bounded by the given curves. a)y = 3x2 − 12 and y = 0 b)y = x2 − 2 and y = 10 −…

A: we have been given the function y=3x2-12 and y=0 and the formula of the area under the curve is…

Q: 4/2 x2 -1 for [0, 1]. Find the length of the curve y=- Find the area of the curve bounded by the…

A: (7)We will find the length of the curve.

Q: 9. Find the area of the region between y = sin 0 and y = sin e , between 0 = 0 ande = n/2. %3D

A: To find the area of the region between,  y = sin3 θ  and y = sin θ Between θ = 0 and θ = π/2 The…

Q: (b) Suppose we wish to estimate the area 3 Vĩ dx 2 using the Trapezium rule.

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Q: %3D Question 3: Find the area between the curve y = 4 – x2 and the line y = -x + 2.

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Q: 1) Sketch the region enclosed by the given curves and find its area. 1 y = x for x > 0 ||

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Q: 1. Find the area between the curves of y = x² + 1 and y = x + 7 from x = -2 to x = 3. Round to two…

A: (Note: We are entitled to solve only one question at a time) Given: y=x2+1 and y=x+7 x=-2 , x=3. To…

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

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Q: 1)Find the area bounded by the given curves: a)y = 6x2 and y = 24   b)y = 3x2 − 12 and y = 0

A: The given function are y=6x2 and y=24. The area bounded by the given curves as shown below:

Q: Question 2 Area bounded by the curves y=e*, y=e", x=0 and x=In2 (А) 604/9 (В) 304/14 C) 502/9 304/7

A:

Q: 3. Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis…

A: Follow the procedure given below.

Q: 15. What is the appropriate total area bounded by the curve y = sin x and y = 0 over the interval 0…

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Q: 2. Find the area of the region that lies inside both curves * r = 4 sin(0) and = 4 cos(0) 2л — 1 ●…

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Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: 3. Find the area bounded by the curve y = - x² x = 1, and the x-axis. %3D x4 – 16

A: We first sketch the region using a graphing calculator.

Q: QUESTION 4 The area enclosed between the x-axis and the curve y=x² between x=1 and x=2 is:

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Q: (4) Find the area of the region bounded by the curves y = sinx, y = cos I, I = T x = 3π/2. You will…

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Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: 2. Find the area bounded by the curve ay² = x³ and the line x = 4 a. 3. Find the area of half an…

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Q: 25) Find the areas of the regions eoclosed by the lines and curves y 2 sin x and v sin 2x, 0SIST

A: To find the area enclosed by the given curves: y=2 sin x and y=sin 2x, 0≤x≤π The area enclosed by…

Q: If we want to find the area under the curve of y = sin(x) + cos(2x) when x is between 0 and , what…

A: In this question, we want to know the formula to find the area under the given curve.

Q: 17 1. Find the area between the curves y=- 9+x* 13 and y = 1+x*

A: Here we have to find Area bounded by the curves y=179+x2..................... (1) and y=131+x2…

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.