Find the area under the graph of f over the interval [3,8). 4x + 5, for xs6 f(x) = - 35 - x, for x>6

Q: Find the area under the graph of y = -x² AL 54 3-2 -11° 1 2 3 4 5 X 4x on the interval [-4, -2].

A: We will solve the required.

Q: .Find the area under the graph of y = g(x) from -3 to 6, where x², g(x) = 18 – x, x > 2

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Q: Find the area under the graph of f(x) = 1+x² from x = -2 to x = 1 using 6 rectangles and right…

A: Area under the graph and Right hand sum of given curve  F(x) = 1+x2 under interval [-2,1] can be…

Q: Find the area under the graph of f(x)=4-x2  on the interval[-1,2]

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Q: What is the net signed area between f(x)=2x+4 and the x-axis over the interval [−7,4]? Do not…

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Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

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

Q: Find the area bounded by x²y = x² - 4 and x-axis, from x = 2 to x = 4.

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Q: Estimate the area under f(x)=x^3 from x=1 to x=5 using n=4 rectangles and choosing heights via: (a)…

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Q: 2. Approximate the area under the graph of f(x)= 25–x² from x=0 to x= 5 using the midpoints of five…

A: Area of graph under f(x) = ∫05f(x)dx

Q: Find a formula for RN and compute the area under the graph of f(x) = 13x² + 91x over [6, 11] as a…

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Q: Find the area of the region under the graph of f(x) = ln(x) from x = 3 to x = 11.

A: Given function : f(x) = ln(x) To find the area of the region from x=3 to x=11 To find the area of…

Q: Find the area enclosed between f(x) = 0.65x² + 7 and g(x) = x, on the interval from x = -3 to x = 5.

A: Given,  fx = 0.65x2+7 gx = x  We have to find the area enclosed between fx and gx on the interval…

Q: The area under the graph of f(x) = – x³ over the interval [-5, 5] is equal to zero Select one: O…

A: Area under the curve f(x)= integration a to b f(x)dx

Q: Estimate the area under the graph of f(x)=x^2+2x from x=3 to x=11 using 44 approximating rectangles…

A: We have to estimate the area under the graph of f(x)= x2+2x from x=3 to x=11 using 44 approximating…

Q: Compute the area between the x-axis and the graph of f(x)=x(x-1)(x– 2) on [0,3].

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Q: What is the area between the graphs of f (x) = 3x + 5, g (æ): -2x – 3, x = 2, and x = 12?

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Q: Find the area enclosed between f(x )= 0.8x^2 + 9 and g(x) = x from x = −2 to x = 4

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Q: Consider the area under the graph of f (x)=x – 3x, from x = 2 to x= 4. a. Estimate the area under…

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Q: Find the area under the graph of f over the interval [1,7]. 6x +5, for xs6 f(x) = 59-3x, for x>6

A: Given

Q: Find the area enclosed between f(x) = 0.3x² + 4 and g(x) = x from x = -3 to x = 4.

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Q: 2. ) Find the area below f cx) -x +7x*- 1o x +3 over the interval 1L x<2 (Drow and Illustrate the…

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Q: 1 Estimate the area under the graph of f(x) over the interval [1, 5 using four %3D x + 4…

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Q: What is the total area between f(x)=−x−4 and the x-axis over the interval [−8,6]

A: Given that the function fx=-x-4. Find the total area between the given function and the x-axis over…

Q: 8. Find the area bounded by f(x) = (2x² – 9)(2x – 3) on [-2,1].

A: It can be solved using application of integration. To calculate area under a curve f(x), follow…

Q: What is the net signed area between f(x)=2x+3 and the x-axis over the interval [−4,2]? Do not…

A: Please see the attached pic. The given line f(x) = 2x+3 has been plotted. The range [-4,2] is shown…

Q: Find the area enclosed between f(x) = 0.6x² + 3 and g(x) = x from x = -2 to x = 6.

A: Topic:- application of integration

Q: 1. Find the area bounded by the two curves f(x) = x2 - 5 x + 6 g(x) = x + 6

A: Given curves f(x)=x2-5x+6g(x)=x+6

Q: Find the area of the region under the graph of the function f on the interval [0, 10]. f(x) = 10x -…

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Q: Compute the area under f(x)=9x1/2+54x-2 and above the x-axis on the interval from x =1 x=36.

A: Explanation of the answer is as follows

Q: What is the net signed area between f(x)=−2x−6 and the x-axis over the interval [−8,2]? Do not…

A: f(x)=-2x-6 First we graph the given function  Then we look at the intervals to find out the area

Q: Find the area under the graph of f(x) = 4-x² on the interval [-2, 1].

A: The given function is f(x)=4-x2 and the interval is -2,1. Draw the graph of the function f(x)=4-x2.

Q: Find the area under the curve f(x) = 3x+ 1 over the interval [2, 6] with n = 4 by using right end…

A: Given f(x)=3x+1, a=2, b=6, and n=4.

Q: 2. Find the area between the graphs of the functions f(x) = 8 – 2a2 and 9(x) = 4 – x? over the…

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Q: Find the area under the graph of f over the interval [- 1,4]. 2 x +2 x2

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Q: a) Estimate the area under the graph of f(x) = 6/x from x = 1 to x = 5 using four approximating…

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Q: 9) Given the function f(x)=-x+4 , find the net signed area between f (x) and the x-axis over the…

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Q: 5. Find the area of the region bounded by the xr-axis and the graph of f(x)= -over the interval (-o.…

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Q: Find the area under the graph of f over the interval [5,7]. |8x + 5, f(x) = for x6

A: Area of function is found by integration

Q: Find the area bounded by f(x) = -x² +4x +1 and g(x) =x+1

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Q: What is the area between the graphs of f (x) = 3x + 5, g(x) = -2x – 3, x = 2, and x = 12?

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Q: (A) Estimate the area under the graph of 3 f(x) = from x = 1 to x = 5 using 4 approximating…

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Q: b) Find the area enclosed between f(x)= = -x² + 4x and g(x) = x² - 6x + 5, over the interval 0≤x≤ 1.

A: Sol

Q: 5. Find the area bounded by the graphs of f(x) = x2 – 3x – 10 and g(x) = x + 2 %3D -

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Q: Approximate the area under the graph of f(x) = 0.03x* - 1.44x + 43 over the interval [3,7] by…

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Q: nd the area under the graph of f over the interval [-2,4]. x +4 xs2 f(x) = 4x x> 2

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Q: Find the area under the graph of f over the interval [-2,4]. .2 X+6 XS2 f(x) = %3D 5x x> 2

A: To find the area under the graph of the function fx over the interval -2, 4.fx=x2+6,   x≤25x,…

Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

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Q: Compute the area under the curve of f(x)=e^4x − 1/x from x=2 to x=5

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Q: Compute the area under the curve of f(x)= e4 1 from x = 2 to x = 5

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Q: Find the area under the curve  over the stated interval. fx=x^-2/3;[1,27]

A: Area under the curve f(x) between the interval [a,b] is given by:

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.