(b) Find the area of the curve f (x) 1 .between the value 1 and 5 using (i) Simpson's %3D 1+x2 1/3 rule (ii) Simpson's 3/8 rule. Comment on their values. Tunioin the snecial features of Muller's and Secant method to find a real root of a

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Q: 11. Find the area bounded by the curve 5y²-16x and the curve y²=8x-24. A. 30 sq.units C. 16 sq.units…

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A: Given data: *The end of the parabolic water tank is in the shape of the region inside the graph of…

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A: a) The given functions are fx=x22-4xgx=-x2+8

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Q: 2. Sketch the curve y=3x²+1 between x=-2 and x=4. Determine by integration the area enclosed by the…

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Q: a) The region R lies inside the curve r v2 sin 0 (for 0<0 <n) and outside the unit circle r = 1.…

A: We have to sketch the region R which lies inside the curve r=2 sinθ for 0≤θ≤π and outside the unit…

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A: First of all, consider the graph for curve y, the coordinate axes and the vertical line x = b.The…

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A: Sketch the graph and integrate function in given interval.

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

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Q: 3. the first quadrant area bounded by the curve r=a sin 2 0

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A: Area

Q: 1) Find the area enclosed by the given curves y region first. Show all your work for full credit.…

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Q: The ends of a "parabolic" water tank are the shape of the region inside the graph of  y = x2  for  0…

A: The height of the water, y varies as water is pumped out of the tank.The width of the tank for any y…

Q: 5. Suppose a is a positive real number. Determine the area of the triangle enclosed by the lines y =…

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Q: Find the area of the surface formed by revolving the graph of f(x) = sin x on the interval [0, |…

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Q: 3. 2. 1. 5 3 T 5л 4 4 4 2

A: Given,  f(x) = 2−cos(x) To find the antiderivative of f(x) ∫f(x) dx = ∫(2-cosx)dx                  =…

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A: Given:    Parabolic water tank is given with the conditions

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A:

Q: Given the curves y= - 4.x and y= -x² + 8, (a) Sketch both curves on the same coordinate plane…

A: Consider the curves, y=x22-4x    and    y=-x2+8 To Sketch both curves on the same coordinate plane…

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Q: Find the exact area of the region inside r = 4 + 4sin(0).

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Q: Л 5л nd the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-. 4 4

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A: Given Data The equation of a curve is y=sin x. The interval is 0≤x≤π.   The expression for the area…

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A: according to our guidelines we can answer only three subparts and rest can be reposted.

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Q: π 5″ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x = 4 4 A.…

A: This question can be solved using the concept of area bounded by two curves.

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Q: 1. Find the area between y=x and y=x' fromx=-1 to x-1. 2. Find the area of the "triangle" region…

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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: 3. f(x) = -x³ + 2*, with 0 <x< 2. a. Approximate the area under the curve using the Midpoint Rule…

A: Answer is mentioned below

Q: etermine the area bounded by the curves f(z) = 1² – 18x + 36 and g() = -9x + 18.

A: This question is based on application of Integration.

Q: Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and…

A: Given: Find the area of the “triangular” region in the first quadrant bounded on the left by the…

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Q: The “arc length function” for a curve y = f(x), where f is an increasing function, is s(x) = √(3t +…

A: Arc length of a function f(t) from t=0 to t=x is∫0x1+f'(t)2dt         ⋯(1)

Q: a. Set up an integral for the length of the curve. b. Graph the curve to see what it looks like. c.…

A: Explanation of the answer is as follows

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A:

Q: 1 2 1. Find the area bounded by the curve y =x² + 5, the x-axis, and the vertical lines x = 2 and x…

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Q: Find the area of the region bounded by the two curves: y = sin 2r, y = tan r, for z 20, and r< 2.

A: Here, y=sin(2x) , y=tanx , 0≤x&lt;π2 Region bounded by these two curves in the interval 0≤x&lt;π2 is…

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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.