Estimate the area under the graph of g(x) = x² from x = 1 to x = 3 using four approximating rectangles and right endpoints. a. Sketch the graph of g(x) = x² with the four rectangles. b. Find R4.

Q: Find the area under the graph of the function f (x) = xe-* between x 0 and x = 5.

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Q: 18.Find the area bounded by the graph y = 30x – 3x² and the x – axis. %3D

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Q: 1. Find the area in the first quadrant bounded by f (x) = 4x – x² and the x-axis.

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Q: Draw the graphs and find the between the area curves f (x) = (-1)**'x² + (-1)**' (b+3)x+(-1)°(c+5)…

A: This problem is an application of Definite Integrals and I find the area enclosed between the curves…

Q: Approximate the area under the graph of f(x) = x' over [1,3] by using N = 4 with left endpoints. 20…

A: The objective is to estimate the area under the graph of fx=x3 over the interval 1,3 by using N=4.…

Q: 7) Find the area under the parabola y = x² – 2x +2, above the x-axis and between x = 0 and x = 1.

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Q: Find the real number b 7 0 so that the area under the graph of y = x3 from 0 to b is equal to 4.

A: The area under the curves y = x3 from x =0 to  x = b is given by integral ∫0bf(x)dx The value of b…

Q: Find the area under the graph of f(x)= x2 and above the x-axis, between x = 0 and x = 3.

A: Given, f(x) = x2, we have to find the area under the graph f(x) and above x-axis between x = 0 and x…

Q: Calculate the area, in square units, bounded above by f(x)=x2+8x+16 and g(x)=8x+80 and bounded below…

A: The solution of the problem is given in the next steps.

Q: ii, Find the area under the graph y=5x⁴between the limits x= 1 and x=3.

A:

Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles…

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [-1, 2] by…

A: Clearly the given integral can be approximated by the areas of the given triangles.

Q: Find the net signed area between the graph of the function f(x) = |x +3| – 4 and the r-axis over the…

A: Given: f(x)=x+3-4 and the x-axis over the interval -9, 3 To find the net signed area between the…

Q: Approximate the area under the graph of f(x) and above the x axis using n rectangles

A: Given function is: fx=4x Number of rectangles is n=4. Limit of x is, a=2 b=6

Q: Calculate the area between the graph of f(x) = x² – 36 and the x-axis given x E [-4,6]. 200 а) - 3…

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Q: 2. Find the area enclosed by the curve y2 = x6 (1- x²)³.

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Q: Approximate the area under the curve of y = x² - 2x + 3 over the interval x = -1 to x = 3 using 4…

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Q: Let f(x)=3x°. /16 – x* - The area between the graph of f and the x-axis, on the interval [0,2] is..

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Q: Say the function g(x) = ;x + 2. Approximate the area bounded by the graph of y = g(x) and the x axis…

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Q: Find the area bounded by f(x) = 4x − x2 and the x-axis. (In square units)

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: 1. Find the area lying above the x-axis under the parabola y = 4x – x2.

A: The area lying above the x-axis under the parabola y=4x-x2

Q: Let f(x)=-2x^ 3 +6x^ 2 -x+1, Use L 4 to estimate the area under the curve or the interval [- 1, 1]…

A: L4 is the left endpoint of the expression with 4 approximating rectangles.

Q: Q2/ Find the total area between the curve y = -x² – 2x and the X-axis.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the area between the graph of y = and the x-axis for x e [0, b] where b is a (2x2 + 1)2…

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

A:

Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [0, 3] by…

A:

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(x) = 3x2, above the x-axis, and between x = 0 and x = 2.

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Q: Find the area between the graph of y = 3x2 + x and the x-axis for x=0 to x=1. %3D

A: From the given curve the bounded region is shown below:     Now using the double integral method to…

Q: 1. Find the area under the parabola y = 8 – x 2 – 2x, above the x-axis.

A: Given parabola y=8-x^2-2x Area = double integral (dx dy). First we will draw the graph based on…

Q: c) [ 1: Estimate the area under the graph of f(x) = x² - 1 from x = 1 to x = 3 using four…

A:

Q: Q2. Find the area enclosed by the function e and the x-axis.

A:

Q: Draw the graphs and find the area between the curves f (x) = x - x+3 and g(x) = -4x+1.

A: Let's find.

Q: Find the area bounded by the line f(x) = 3x – 5, the curve g(x) = x² – 10x + 7, and the two vertical…

A: Area between two curves :   If f(x) and g(x) be the two continuous function on a,b and f(x) ≥g(x) on…

Q: Use the Fundamental Theorem to determine the value of b if the area under the graph of f(x) = 4x…

A:

Q: Approximate the area under the graph of​ f(x) and above the​ x-axis using n rectangles. f(x)=6/x…

A: The width of the interval [2, 10] is = 10-2=8 There are 4 partitions. So the width of each…

Q: Use a graphing calculator to approximate the area between the graphs of y = In x and y = 9x e* on…

A:

Q: 1. Find the area enclosed between the graphs of y = 5 – 10x + 7x? – a3 and y = 4x – 3.

A: given equations are

Q: Q2. Find the area enclosed by the function e* and the x-axis .

A:

Q: Use the Fundamental Theorem to determine the value of b if the area under the graph of f(æ) = 4x…

A:

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [– 1, 2] by…

A: Given the graph of the function :

Q: Find the exact area between the curve f (x) = x³, the x-axis, and x=0 and x=4.

A:

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by…

A: Given function is f(x)=9-x2 we have to find the area over interval [0, 3]. Since there is 3…

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: For F(x)= 3+3x-2x^2 A. Sketch the graph and the rectangles from x=0 to x=2 using n=4 and right…

A: The given function is:…

Q: Find the area between the y-axis and the graph X = -y + 5y – 4 on the interval [1, 4]. 3- 2- 54 3-2…

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Q: 4. Find the surface area of the function x when revolved around the x-axis. between x=0 and x1

A: When a curve is revolved about an axis, we obtain a surface and there are several pre-defined…

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x? over the interval [– 2, 1] by…

A:

Q: Find the area between the curve y = x = 0 and x = 5. x(x 3) and the ordinates - LA B 3

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.