Find the area enclosed by the x-axis and the given curve.x = 4 + ety = t - t2

Q: QL. Find the area under the curve for following equation for the interval (x= 0 to x = 8) 1 y = (x-…

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Q: Find the area between = (x-2) e and the x axis from x = 2 to x 6. Select the correct answer. t e?…

A: To find: Area between the curve y=x-2ex and x axis between x = 2 to x = 6

Q: Find the area bounded by the curve y = x^99 the, the axis and the ordinates x = 0 and x = 1. a.…

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Q: Find the area of the shaded region. 10 e e 3 y 3- x = y - 4 y = 1 X = -2 4 y = -1 3.

A: The shaded region is the area between the curves x=y2-4 and x=ey where -1≤y≤1. That is,…

Q: Find the area under the graph of the function over the interval given. 18) y = 2x +7; [1, 5] A) 18…

A: We can find the area as below.

Q: Find the area enclosed by the curve x= t2-2t, y = √t and the y-axis.

A: The area enclosed by the curve x=t2-2t, y=t and the y-axis

Q: Find the surface area of the figure when d = 4 cm. For calculations involving x, give both the exact…

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Q: Find the area bounded by the given curves and lines. y? (2-a) x = -2 | x = 0

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Q: find area for given data  z less then 0.1653

A: From the provided information, The area is z < 0.1653 that is P (z < 0.1653)

Q: Given the function, find the area between the graph of the function, the x axis over the interval…

A: Just integrate this function from 1 to 4.

Q: The area bounded by the curve y=4- x2 · x-axis and the line is? 16 Ob. 11 Oc. 16 Od. 1 а. 5 3 3 3

A: The graph is shown below:

Q: Find the z-value when the area from 0 to z is 0.4378 a. 1.84 b. 1.90 c. 1.94 d. 1.98

A: Given : Area from 0 to z = 0.4378

Q: Find the z-value such that the area in the left tail is approximately 0.27.

A: Z - score : Z is also called as standard normal variate as it follows normal distribution with mean…

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

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Q: Find the area between x = y^2 - 4, y = e^x

A: To find - area

Q: Q2. Find the area enclosed by the curve y = x³ – 3x² + 2x and the x-axis.

A: To find the area enclosed byy=x3-3x2+2x and x-axis

Q: Find the area bounded by the curves x² + y? – 2x – 24 = 0 y2 – 8x + 16 = 0

A: The area between two curves y1 and y2 such that y2>y1 between the limits x=a to x=b is given by;…

Q: b) Find the area under the curve given by g(x) = x? + 4x between x= 6 and x = 9.

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Q: Choose which of the following is the EXACT value for the area bounded by y = e" and y = -e' on the…

A: The region is bounded by y=ex and y=-e-x on the interval 1≤x≤2

Q: y = e2x, y = e*, and x = 2

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Q: Find the area bounded by the curve a?y = x3 the x- axis, and the line x-2a. Solve with respect to x.…

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Q: FIND THE AREA BOUNDED BY THE WRVE ay THE x-AXIS AND THE UNE X- 2a.

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Q: Find the area enclosed by the x-axis and the curve y = -x2 + 9. A.) * 32 s.u. В.) 18 s.u. C.) 36…

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

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Q: Find the area between the curves y? = -12x and y? = - 24x – 36.

A: y2=-12x,  y2=-24x-36 find intersection points -12x=-24x-36 -12x+24x=-36 12x=-36 x=-3 . y2=-12x…

Q: Find the area betwen the following curves.  x = -3, x = 1, y = x3 + 8, and y = 0.

A: Answer and explanation is given below

Q: Find the area enclosed by the y-axis and the curve x = t - t2, y = 1 + e-t .

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Q: 4) Given the trapezoid shown, express the area in terms of x. - x+1 r+5

A: We have to find the area of trapezoid in term of x.

Q: Find the area enclosed by the given curves y= x?,y = x 2 + 6, x = -2, and x = + 2 32 16 4 O00O

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Q: x = -Jy from y = 1 to y = 4

A: The objective of the question is determine the area bounded by the given function.

Q: Find the area between the following curves, 3. x= 1, x = 3, y =x-8, and y= 0 Area =(Type an integer…

A: Giveny=x3-8x=1 and x=3 and y=0To findArea

Q: Find the area bounded by the following curves, y = x^2/4 and x + 4 = 2y. a.6 b.7 c.8 d.9

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Q: Find the area bounded by the curve c²y=x³, the x – axis, and the line x =2c.

A: We find the area bounded by the curve using the integration. Before finding the area, first, we will…

Q: Find the exact area between y=x3 and y=x for x≥0.

A: The graph of given curves: The shaded region of the above figure represents the area between the…

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

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

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Q: b) Find the area bounded by the – axis, y = x and y = 2 – x.

A: Area bounded by the curves

Q: 3. Find the area in the first quadrant under the curve 1 y = 1+x

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Q: Find the area bounded by the curve y=x^2, the axis, and the ordinates are x=1 and x=3.

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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: Find the area enclosed by the given curve and the y-axis.x = t2 − 3ty = square root of t

A: From y=sqrt(t) find t=y^2Then plug it in x=t^2-3tSo the curve is: x=y^4-3y^2

Q: Find the area between the curve and the x-axis over the indicated interval. y = 6 x 10 [1, 10] The…

A: See this solution in below

Q: Find the total area of the region between the curve and the x-axis. y = (x + 1)3; 0 s xs 4 O A) 156…

A: The solution are next step

Q: Find the area that corresponds to the z-score and sketch the curve. 1. to the left of z = -1. 05…

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Q: Find the area of the shaded region. Ay 42 = 4 csc e cot e 0- 3x 4 -4/2 of

A: Consider the given graph. The shaded region is bounded above by the straight line parallel to the…

Q: Find the area bounded by the curve x² =16y and the x axis from x = 1 to x = 3. A. 0.5917 C. 0.5417…

A: We can find the area bounded by the curves. Note : As per our Guidelines we can solve first…

Q: Determine the area of the region between the two curves in the given figure by integrating over the…

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Q: Find the value of a such that the area bounded by y = e−x , the x-axis, x = −a, and x = a is 8/3.

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Q: the area bonnded by y=X y-X

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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.