Consider the function g(x)=5x2−18x+35. Find the area under the curve g(x) from x = -5 to x = 15 and then subtract from it the area under the same curve g(x) from x = -5 to x=1. What is the difference?

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

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Q: Consider the function f (x) = –x² +9. What is the approximation of the net area under the curve of f…

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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: 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 area between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x =

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Q: Estimate the area between the x-axis and the graph of f(x)=9−x2f(x)=9-x2 over the interval…

A: We will use rectangle's formula to evaluate the area of curve

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: "In Computing the area between two curves, why does f(x) have to be greater than g(x) over the…

A: In computing the area between two curves, why does f(x) have to be greater than g(x) over the…

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

Q: The area under the graph of f(x) = 3x2 between x = 2 and x = k is 208, where k> 2. Find the value of…

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Q: Find the exact area between the graphs of f (x) = 2x +1 and g (x) = 9 – x2. First find out where the…

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Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: First, we need to find the points of interesection of f(x)=7x2+3x−45 and g(x)=8x2+22x+45At points of…

Q: (a) Estimate the area under the graph of f(x) = 7 + 2x2 from x = -1 to x = 2 using three rectangles…

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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 total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

A: To find the total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: The given functions are,

Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

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Q: Find the area bounded above by the function f(x) = -3x² + 4x - 1 and bounded below by the x-axis.…

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Q: Consider the region bounded above by f(x)=−2x3−9x2−10 and below by g(x)=−x3−12x2−10. Find the area,…

A: To calculate the area contained between the two given curves (as boundaries)

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

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Q: Find the area of f(x) = 3 +2x – x² above the x-axis.

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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: Approximate the area under the following curve and above the x-axis on the given interval, using…

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Q: Calculate R3 and L3 for f (x) = x2 − x + 4 over [1, 4]. Then sketch the graph of f and the…

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Q: f(x) = 3 + 2x2 from x = −1 to

A: Given: f(x)=3+2x2 from -1, 2

Q: Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis.

A:

Q: Find the total area between the curve of the function f(x)=2x+4 and the x-axis over the interval…

A: We have to find the total area under f(x)=2x+4 and the x-axis over the interval [−9,−1]Recall that…

Q: Estimate the area under the graph of f(x) = 7 + 4x^2 from x = -1 to x = 2 using three rectangles and…

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Q: Estimate the area under the graph of f(x) = x + 2x from x = 5 to x = 11 using the areas of 3…

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Q: Question in image along with part (a) repeated using left points and midpoints.

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Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

A: The function given is  f(x)=2+4x2 on the interval [-1, 2]

Q: Given the graph of the function f(x) below, use a midpoint approximation with 4 rectangles to…

A: Width of each interval = (6-2)/4= 4/4= 1 So the partition is 2 , 3, 4, 5, 6 So the midpoints are 2.5…

Q: Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and…

A: In this question, we find the area by using the midpoint rule for the given function f(x)=4+4x2 for…

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…

Q: find the area between f(x)=x^2-16 and the x axis from x=0 to x-=9

A: The given function is fx=x2-16 We have to find the area between fx and the x-axis from x=0 to x=9

Q: (a) Estimate the area under the graph of f(x) = 7 + 2x² from x = -1 to x = 2 using three rectangles…

A: We have to estimate the area under the graph of f(x) = 7 + 2x^2 from x = -1 to x = 2 using three…

Q: Given the graph of the function f(x) below, use a midpoint approximation with 3 rectangles to…

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Q: Find the area above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

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: 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: (Area Under a Curve)

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Q: Find the area between the curves of the functions f(x) =4x - x² and g(x)= x² -6x +8. Round to 1…

A: Use double integral

Q: 1. Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Solve. 1. Find the area of the region between the function f(x) = 4x + 1 and the x– axis on the…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the area (sq. units) covered by the line y = -Gx+ 3) from x1 = -8 to x2 = 0.

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Q: Consider the region bounded by f(x)=−x2+11x−3 and g(x)=5x+5. Find the area, in square units, between…

A: Given:

Q: Find the area between the curves f(x) = x^2 - 4x +12 and g(x) = x^2 - 2x + 2  for 0 ≤ x ≤ 3

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

A: The given function f(x)=9-x2 over the interval [0,3]

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.