2. Consider the region R bounded by the graph y = r' + 8r, the r-axis, and the vertic lines z = 0 and r = 2. (a) Sketch the graph on the indicated interval, and indicate the region R clearly. (b) Find the area of region R using the definition area = lim f(right,)Ar.

Q: 2/ determine the area of the region enclosed between the curves x= 0sy'-3 and y=x-1? ans/ 18

A: Please see the explanation below

Q: 5. Determine the point intersection between curve y= x(3-x)and the line y= x. Hence, find the area…

A: To find the intersection points of the given equations y = x(3-x)  and y = x

Q: Determine the area of the region bounded by y = sin x and y = cos x over the interval [0, 2n] and…

A:

Q: 4 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

A: See below attachment.

Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = x…

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Q: y = 0, y = cos 2x, on the interval li [引 %3D

A:

Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

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Q: The area of the region bounded by the curves y=x and y= 20-x² is

A:

Q: The area of the region bounded by the curves y =x and y= 20-x² is

A:

Q: Find the area of the region bounded by the curve 2-4r and the lines x = 1 and x = 4.

A: To find the area

Q: 27 Find the area of the region bounded by, 4 a. The curve y= and the line y = 5 – x. b. The curves…

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Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1?

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Q: 27 Find the area of the region bounded by, 4 a. The curve y=- and the line y = 5-x. b. The curves…

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Q: Find the area of the region between the curves y=x^3, y=-x, and y=1

A: Area=14 sq.units

Q: Sketch the region bounded by the graphs of the equations y = x2 − 1, y = −x + 2, x = 0, x = 1 and…

A: Sketch the region bounded by the graphs of the equations y=x2-1,y=-x+2,x=0,x=1 as shown below.

Q: Sketch the region enclosed by the given curves. y = tan(9x), y = 2 sin(9x), -1/27 sxs 1/27 У 3 3 0.1…

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Q: 1. Find the area of the region enclosed by the line x = 2y and the curve x = y - y?

A: We will find out the required area.

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

A:

Q: 4. Find the area of the region bounded by the line y=x and the curve y=x^3. Show the region.

A: Draw the region and find intersection point then integrate

Q: Find the area of the region bounded by the curves: y = cos(nx) and y = -1 + 4x2

A: The region between these two curves is shaded below

Q: Sketch the region enclosed by the given curves andfind its area.   y - cos πx    , y=4x2- 1

A: The given curves are y=cosπx   and  y=4x2-1. Sketch the region enclosed by the above curves as shown…

Q: Sketch the region enclosed by the given curves. y = 3 cos(9x), y = 3 – 3 cos(9x), OSxS1/9

A: Solution is in step 2

Q: 27 Find the area of the region bounded by, b. The curves y=x-5x and y 25-x

A:

Q: find the area of the region bounded by the curve y^2=x+1 , both by the x and y axes and the line x=8

A: Using Reimann sums, the area of the region R is given by Sn=∑k=1n∆Ak. This is simply the sum of…

Q: Sketch the region enclosed by the curves y = 2 sin(x), y = 2 csc²(x), x = 7 and x = 4, and compute…

A: The given curves are: y=2 sin x,       y=2csc2x,       x=π4      and      x=3π4

Q: Sketch the region R under the curve y = 4x – x² above the x-axis from x = 1 to æ = 5. Use the…

A: Given problem:- Sketch the region R under the curve y = 4x - x2 above the x-axis from x=1 t x=5 Use…

Q: 3 Find the area of the region bounded by 2x = y²+1 and the y-axis using the horizontal strip.

A: The given region is bounded by 2x=3y2+1 and the y-axis.

Q: 7. Sketch the region enclosed by the curves x = region. y4 and y = V2 – x for y > 0 and find the…

A:

Q: Find the area of the region between the curves y = x + 1, y = 9 – x², x = -1, and x :2. %3D Area…

A:

Q: Sketch the region bounded by the curve y = x(x – 1) and the linear equatio x at (-1,2). Calculate…

A: Given: y=x(x-1)

Q: Find the area R -region bounded by the curve y=1/x^2 and the lines y=x and y=x/8.

A:

Q: 8 Determine the area of the region bounded by the curves y = =, y = 2x and x = 4

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Q: Find the area of the region bounded by the curves: y = cos(nx) and y = -1+ 4x²

A:

Q: 1. Find the area of the region bounded by the curves y = |x² - 4| and the curve y =x2 + 4 %3D

A: One of the two main parts of calculus is concerned with the study of integrals, as opposed to…

Q: Find the area of the region enclosed between the curves y= 4 -x^2 and x=3 and x-axis within the…

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Q: Find the area of the = -, y=3-k| region that is restricted between is curves.

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Q: Sketch the region enclosed by the given curves. y = 7 cos(2x), y 7-7 cos(2x), 0 sxs x/2

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Q: Determine the area of the region bounded by the graphs of 1) y = Cos x, y = Sin x in the interal 0,4

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Q: 3 cos(9x), y = 3 – 3 cos(9x), 0 s xs x/9

A:

Q: Find the area of R - region bounded by the curve y = 1/x2 and the lines y = x and y = x/8 O 1

A: Given: The curve y = 1x2 and the lines y = x and y = x8. To find: The area of the region bounded by…

Q: Sketch the region enclosed by the given curves andfind its area. y = 12- x 2   , y = x2 - 6

A: Given curves are y=12-x2y=x2-6

Q: Find the area of the region between the curve y = √2x — 1 and the lines x = 1 and x = 5.

A: Given: The region between curve y=2x-1 and lines x=1 and x=5

Q: Consider the region bounded by the curves y = x2-4x+5 and y = x +1.  Find the area of this region.

A: Follow the steps.

Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = and…

A: Given curves are: y=x2 ............(1)y=10x-16   .........(2)

Q: (d) Sketch the region bounded by the curve y = sin 2x, y = cos x and the line x=0 and x = 2 %3!…

A: Area of the region is shaded below.

Q: Find the area of the region bounded by the curves: y = cos(nx) and y = -1+4x2

A:

Q: y=√x, x = 4, and the x-axis.

A: Consider the given function y=xand the x-axis

Q: Find the area of the region between the curve y =53-* and the interval [0,2] on the x-axis.

A:

Q: Sketch the region bounded by the graphs of the equations and find its area. y =x² +1; y=x+1

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.