Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.  Between y = x3 and y = 1 for x in [−1, 1]

Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11. 4. Determine the area to…

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Q: Find the area under the curve -2.5 Y = 1.5x from x = 6 to x = t and evaluate it for t = 10 and t…

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Q: Find the area of the shaded region below. yA x=y² - 2 y 1 x=e y=-1

A: Given: Eq1 : x = ey  Eq2 : x = y2 - 2  Limit y = -1 to y = 1

Q: Find the area under the curve y = 1/(4x) from x = 1 to x = t and evaluate it for t = 10, t = 100.…

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Q: #1 Find the area of the region between y=2x+ and y=x=4

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Q: f(x) = x^3 + 4x and g(x) = 6x^2 - x Find the area between the two curves

A: We have to find the area between the given curves.

Q: Find the area enclosed by the given curves. Find the area of the region between the curve y = 4x/(1…

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Q: Find an expression for the area between the curves y = x-/2 and y = e between the lines X = 0 and x…

A: In this question we have to find the expression for the area between the curves.

Q: Solve this attachment.

A: From the figure, the integral to obtain the area can be represented as, ∫-11y2-2-eydy

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

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Q: Find the area of the shaded region below. yA x = y² - 2 y 1 x=e' y =-1

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Q: 12. The area enclosed by the two curves y=x-4 and y =x-4 is given by (a) [(x-x)dx (b) [(x²-x)dx (c)…

A: y=x2-4  &  y=x-4 The graph is,

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

A: Given curves are y=f(x)=e^3x,y=g(x)=e^x and x=ln8.Firstly, we find point of intersection of f(x) and…

Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: Kindly help

A: The area bounded by the curves are y = e2x, y = ex and x = ln 4 in the first quadrant.Use the above…

Q: The area of the region bounded by y-19-x, the x-axis and the line y-x in the first quadrant is: O…

A: Given: y=9-x2 y=0 y=x Calculation: Use an online graphing calculatora and obtaine the bounded region…

Q: Find the area between the curves 2 e 3x, y= e 3x+e6 -0, x 3, y The area between the curves is…

A: Given

Q: Find the area, if it exists, of the region between the curve and the x-axis on the given interval.…

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Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

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Q: 1. Find the area of the shaded region analytically (without a calculator). y= 0.5sec² (x) 3 2…

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Q: Find the area under the curve -3 y = 2x from x = 8 to a = t and evaluate it for t = 10, t = 100.…

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Q: Find the area under the curve y = la-2 from x = 6 to x = t and evaluate it for t = 10, t = 100. Then…

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Q: The area of the region between the graph of y 4z+2 and the x-axis fromx=1 to x 2 is 36 B 23 C 20 D…

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Q: Q. 2. Find the area of the region in the first quadrant that is bounded above by y = Vx and below by…

A: We will use double integration to solve the following problem.

Q: Find the area under the curve -2 y = lx* from x = 6 to x = t and evaluate it for t = 10, t = 100.…

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Q: Find the area between the curves of the following functions. First graph, then find the area. The…

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Q: A rectangular closed box with square base is to have a capacity of 64 cu. in. We want to determine…

A: Given:     Volume = 64       Base = x        Height = y

Q: S(x) = e*. g(x)=e* Calculate the area of the region between the curves and the line x = In 2.

A: The region is given by

Q: Find the total area between the curve y = x³ and the X-axis between x = -2 and x = 2. y = x3 а) b) 8…

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Q: c) Find the area between: y = 2x + 3 and y = -x² + 10x – 9 %3D

A: We first sketch the region using a graphing calculator The functions intersect at x=2 and x=6

Q: Find the area between the graph of this equation and the t-axis. R'(t) = 200e^0.5t for 0 ≤ t ≤ 10.

A: to find:- Area.

Q: Could I get help with the areas of A-D please?

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Q: Approximate the area under the graph of​ f(x) and above the​ x-axis with​ rectangles, using the…

A: As per guidelines, i can answer only three subparts of a question. To know rest, please re upload…

Q: (a) The area to the left of the endpoint is about 0.14. Round your answer to two decimal places.…

A: (a) Consider that the area to the left of the end point is about 0.14 The end point is,

Q: Find the area of the region between the curve and the​ x-axis. f(x)=1−x2​, from −3 to 3

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Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 22. Find the area of the shaded region for the function 4e* y = 1+e23 2x

A: The area of shaded region is given by the integral ∫x=ax=b fx dx=∫0ln 34ex1+e2x dx. Let t=ex. This…

Q: Given function y = f(x) = x2 − 2x − 3. Find the area of the region enclosed by the curve y = f(x),…

A: Answer and explanation is given below..

Q: 0.4 ソミーxe"* -1 -0.5 1.5 --0.2 -0.4 21

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Q: Find the area enclosed by {x=t3/2+t+6 & y=-t2+5t-4} and the x-axis

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Q: 17. Find the area enclosed by the x-axis and the curve y = -x² +9 32 s.u. а. 3 b. 18 s.u. с. 36 s.u.…

A: Find the area enclosed by the x-axis and the curve y= -x2+9

Q: The positive number c for which the curve yd- divides the area under the curve y 2209- from O to 47…

A: Given

Q: Calculate the area between the graph of f(x) = x² (x + 4) and the x-axis given x E [0, 5].

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Q: The total area bounded by the graph of y = x2 –- 1 and the x-axis is represented by :Select one L…

A: The correct option is d. Plot the curves and find the region for the area between the curves. The…

Q: 9- The graph of the function y = x^3 What is the area of the region bounded by the lines y = 0, y =…

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Q: 01:42 d. Calculate the area enclosed by the curve y = 2x2 +3 and the x-axis between x = 0 and x 2.…

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Q: a. (i) Calculate the area of the region enclosed by y = x^2, lines x =1, x = 3, and the x-axis.…

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Q: Find the area of the shaded region. y = e" 4 -1 1 (e - 1)/4 4e 1/4 e/4

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Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

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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.