Find the area of the infinite region in the first quadrant between the curve y = eX and the x-axis.

Q: Find the exact area of the region that lies beneath the curve y = 10x, 0 < x < 27.

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Q: Find the area of the region bounded by the parabola y = x 2  ,the tangent line to this parabola at…

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Q: Find the area of a region bounded by the curves y=e^(2x) - x^3 , the y-axis and x=1

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Q: Find the area of the region bounded by the curves y = e* y² = 4x - 4 between y = 1 and y = 2. and

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Q: : Find the area of the region in the first quadrant that is bounded above by y x and below by the…

A: SOLUTION-

Q: Find the area of the region bounded by the curve y=1- and the x- axis.

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Q: B- Find the area between the curves: x = y2 and y = x - 2

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Q: Find the area between the curves. y = x2 - 18, y = x - 6

A: y = x2 - 18, y = x - 6

Q: Find the area between the curve y=4x-x² and the x-axis

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

A: Now the diagrammatic representation of the area is,

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 area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

Q: Find the area of the curve bounded by the curves y=x* and y=3x+4.

A: We have to find th: e area of the curve bounded by the curves y=x4 and y=3x2+4.…

Q: Find the area between the curve  y = x2 + 3  and the line  y = 2x − 2  (shown below) from x = 0 to…

A: We first sketch the area using a graphing calculator

Q: Find the area of the region between the curves y = x² +9 and y interval [-1,3]. = 10 + 2x over the

A: Given that:                      y=x2+9y=10+2xBetween [-1, 3]   NOTE: As per our answering…

Q: Find the area between the two curves: y = x2 and y = 4x + 5

A: In this question we have to find Area.

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area of the region bounded by the parabola y = 2x, the tangent line to this parabola at (4,…

A: Definition used -              Equation of a tangent line -                  (y-y1)=f'(x1)(x-x1)…

Q: Find the area between the curve :       , and the positive semi-axis "X".

A: Given curve is y=e-xcos(x)

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

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Q: Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A: We have to find the area between the curve y=x3-6x2+8x and the x-axis.

Q: Find the area enclosed by the given curves. y = 2x - x2, y = 2x - 4

A: NOTE: Refresh your page if you can't see any equations. . given functions are

Q: Find the area of the region bounded by the parabola y = x², the tangent line to this parabola at (1,…

A: Given data: The equation of the parabola is y=x2. The given point is (a, b)=(1, 1). The slope of the…

Q: Find the area enclosed by the curve y = x 2 − 3 and the line y = 2x

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Q: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0 -

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Q: Find the area between the curves: y2=x x2– 2x + 3y = 2

A: we have to find the area between the curves :

Q: Find the area between the curve inclosed by the curve x = 2y^2 and the curve x = 4 + y^2

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Q: Find the area of the region bounded by the parabola y=x2 , the tangent line to this parabola at…

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Q: Find the area bounded by the curve 5y^2 = 16x and the curve y = 8x – 24.

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Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: Find the area between the curves x=y² –1 and x = 2y² – 2.

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Q: Find the area between the curves y = x² + 1 and y = x + 1.

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Q: Find the area in the second quadrant bounded by the curve y = x' +4x² – x – 4 and the x – axis.

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Q: Find the area of the region lying between the r-axis and the curve In(3x) – 1 y = to the right of…

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Q: Find the area lying between the parabola y=4x - x^2 and the line y = x.

A: The given curves are y=4x-x2 and y=x. To find the area between the curves we will firstly plot these…

Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

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Q: Find the area of the region between the curve y = 21-x and the interval -1≤ x ≤ 1 of the x-axis.

A: Given: y=21-x, -1,1

Q: Find the area bounded by the given curves. y = x2 − 5 and y = 4 − 8x2 _____________ square units

A: Given curves y=x2-5 and y=4-8x2. The objective is to find the area bounded by the curves.

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

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Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

Q: The area enclosed between the x-axis and the curve y=x2 between x=1 and x=2 is:

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Q: Find the area enclosed between the line y 1 and the curve y = x2 – 4x + 4.

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Q: Find the area between the curves y = 4x – 3 and y = x². %3D

A: Given data is : y=4x-3     .....1 y=x2      .....2 From equation (1) and (2) ,…

Q: Find the area of the region bounded by the curve y = e2x - 3e* + 2 and the x-axis.

A: The region is bounded by the graph y=e2x-3ex+2 and the x-axis.

Q: Find the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

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Q: Find the area between the curve y = 1/x7/6 and the x-axis from x = 1 to ∞

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Q: . Find the area between the curves y =x+1 and y=2x+1

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Q: Find the area of the region between the curves  y= x2 − 4 and y= 2 − x.

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Q: Sketch the graph of the given curves and find the area of the region bounded on the left by the…

A: Graph of x=3-2y2, that is gy=3-2y2 is a parabola as function g(y) is in the form of quadratic…

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

A: Topic = Area

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.