Find the area under the curve y from x = 8x3 1 to x = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for a > 1. (a) t = 10 (b) t = 100 (c) Total area

Q: Find the area between the curve y = x² + 8x + 12 and the x-axis from x = -2 to x = 0. (Give an exact…

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Q: Find the area between y=x+2 and y= x2−1. Round your limits of integration and answer to 2 decimal…

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Q: Estimate x dx using midpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: we have to estimate ∫03x2dx using midpoints for n=4 approximating rectangles.

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A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: Estimate | (2x – 5) dx using left endpoints for n = 3 approximating rectangles. %3D 5 (2x – 5) dx is…

A: Given: ∫152x-5ddx The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: Find the exact value of the area between the graphs of e for 0 < x < 1.9. y = 1 – x and y area =

A: Recall: Area=∫abf(x)-g(x)dx We have, a=0, b=1.9, f(x)=1-x, g(x)=ex

Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₂ = x + 2…

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Q: Estimate the area under the graph of f(x) 1 over the interval [2, 6] using eight approximating x2 +…

A: A function is given by, fx = 1x2+4 over the interval 2,6. The objective is to find the area under…

Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₁ = 1 x²…

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Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

Q: Find the area enclosed by the curves f(x) = 33 - x² and g(x)=x². The area (rounded to two decimal…

A: The region bounded by the curves fx=33-x2 and gx=x2 The formula to calculate the area bounded by the…

Q: Estimate the area under the graph of f(x) 1 over the interval (0, 2 using eight approximating x2 + 1…

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Q: by the x-axis (y = 0)

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Q: 1 Estimate the area under the graph of f(x) : x2 + 4 over the interval [- 1, 3] using ten…

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Q: sin(z)

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Q: Approximate the area between f (x) = x² + 6x + 5 and the x -axis on the interval [0, 2] using 4…

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Q: Find the area between the curve y = x² + 7x + 12 and the x-axis from x = -3 to x = -1. Step 1 Notice…

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Q: Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the…

A: Equation is f(x)=exThe value of the table for x and y x 0 0.25 0.5 0.75 1 y 1 1.284 1.6487…

Q: Find the area between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: Find the area between the curves. y = x5 - 2 ln (x + 5), y = x3 - 2 ln (x + 5)

A: Given: y=x5-2lnx+5y=x3-2lnx+5

Q: Estimate the area under the graph of f(x) = x + 3 over the interval [ - 3, 1] using eight…

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Q: In the diagram below, the region between the graphs of y=2 sin¬x and y=rx, in the first quadrant, is…

A: Finding the area of the shaded region

Q: Estimate the area under the graph of f(x) = 3x2 18x + 28 over the interval [0, 6] using five…

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Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Consider the provided curve,  Bounded above by the curve y=ex2 and below by the curve y=e-x2. And on…

Q: Use four rectangles to estimate the area between the graph of the function f(x) = e² on the interval…

A: For (a),

Q: 22) Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2 sxs2 of the…

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Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the area of the surface formed by revolving g(x) = x^3 on the interval [0, 1] about the x-axis.…

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Q: Estimate the area under the graph of f(1) = over the interval [-2, 3] using ten approximating | I +…

A: The given function is fx=1x+4 over the interval -2,3 using ten approximating rectangles. Calculate…

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Q: Find the area of a region between the z-axis and the graph of f(r) = r² – x² – 2r. Define the term…

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Q: Graph the function y = -0.3x² + 1.5x over the interval [0, 6]. (0, 6] by (-2.25, 2.25] a. Integrate…

A: Given function y = - 0.3x ^ 2 + 1.5x over the interval [0, 6].   To find  a. Integrate y = - 0.3x ^…

Q: 4.1 Can you show me all the steps to solve problem 5?

A: (a) Draw the graph for the function with three rectangles using the right endpoints as shown in…

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Q: Estimate the area under the graph of f(x) = x² – 2x + 5 over the interval [0, 7] using ten…

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Q: 25 dx Evaluate by dividing the interval into 8 equal parts 1 x2 +6x+ 10 by using Trapezoidal rule.

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Q: Find the areas between the curves y = 2(log2 x)/x and y = 2(log4 x)/x and the x-axis from x = 1 to x…

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

Q: Estimate the area under the graph of f(x) = x² + 3x +1 over the interval [1, 3] using four…

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Q: 8) Find the area between the curves: y = x'-9x + 14x and y =-x +9x2 - 14x

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Q: Find the area bounded by y2 = 4a(y - x), y2 = 2a(x + 2y – 3a) and the x-axis. Show complete solution…

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Q: 14. y= sin x with n 6. Round to the ten-thousandths place. on

A: The objective is to compute the area under the curve y=sinx on π4,π using 6 subintervals.

Q: Find the area under the curve y 5 -over the interval [4, 7]. (3x + 1)² Enter the exact answer. area…

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Q: Find the total area between the function f(x)=3x+8 and the x-axis over the interval (−4,−1). Submit…

A: To calculate the unsigned (total area) of the region: in calculating total area, we take only the…

Q: Find the area between the curve  y = x2 + 10x + 16  and the x-axis from  x = −2 to x = 1.  (Give…

A: To find the area between the curve y=x2+10x+16 and the x-axis from x=-2 to x=1. This is given by…

Q: Approximate the area under the curve y=1/x from x=1 to x=4 using the left endpoint estimate with six…

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

Q: The area under the curve y =3/x over the interval [1.4]is equal to: 14

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Q: find the indefinity integral  x^9 dx

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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.