1) Find the area bounded by curve y = xvx2 + 1 and the lines x = 0, x = 4 an %3D the x-axis.

Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: 8. Find the area bounded by x² – 6x + y = 0, - x² – 2x – y = 0, and the x – axis.

A:

Q: 6. Find the area bounded by the curve 2y² + 4x + y = 0 and the line y = 2x.

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Q: 4. Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: 3. Find the area bounded by the curves x2 + y2 = 9 and 4x2 + 9y² 36, on the first quadrant.

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Q: 4 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

A: See below attachment.

Q: 2. The area bounded by y=3x+4 and the curve y=x2 is revolved about the line x =5.

A: 2) The area bounded by the given curves is:

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

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: 1. Find the area in the second quadrant bounded by the curve 2x² + 4x +y = 0 using two methods

A:

Q: 4. Find the area bounded by the curve a²y = x³, the x - axis, and the line x = 2a. Solve in two…

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Q: The area bounded by the curve z = y.y-axis and the lines Y3D0. y32 is s

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Q: Determine the area bounded by the curves y = 6x − x2 and y = x2 − 2x and illustrate an accurate…

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Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

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Q: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

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Q: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

Q: 2. Find the area in the second quadrant bounded by the curve y = x' +4x² –x-4 and the x- axis.

A: To find: The area in the second quadrant bounded by the curve. Given: The equation of the curve is…

Q: 1. Find the area between the curves x2-y = 9 and the line y 2x-6

A: Since you have posted multiple questions in this question which are not interlinked so I do only…

Q: 1. Find the area between the curves x2-y2 = 9 and the line y = 2x-6

A:

Q: 1. Find the area bounded by the curves y – 2 = x² ,y = 6 and the y – axis ( in Quadrant I only), as…

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Q: 9x Area bounded by the curves y=e*, y=e³x, x=0 and x = ln2

A:

Q: 1. Find the area of the region bounded by the curves y = x2 – 3x + 5 and y = 3x + 5.

A: Answer and explanation is given below.. For solution of other questions please repost

Q: 2. Find the area between the curves. x = - 2, x = 1, y = 6x, y = x2 - 7

A: Given: x=-2,x=1,y=6x,y=x2-7

Q: solve the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4

A: To find out the area bounded by the curves.

Q: 8. Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis.

A: We have to find volume of solid generated by revolution.

Q: Find the area between the curves y = e 1. = y = 2.3x + 1 from x = 0 to x = Area -0.4x and

A:

Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

Q: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

Q: 4. Find the area of the region bounded by the curves x-y² = 0 and x+2y² = 6.

A: Hence, the area of the region bounded by the curves x-y2=0 and x+2y2=6 is 82 square units .

Q: 7. Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line p through the…

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Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: Find the area b0 und by Curves the y3= X-3

A: The region is bounded by y=9x2-36, y=0, x=1 and x=3

Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: 11. Find the area bounded by the curve y² + 2x - 2y - 3 = 0 and the y-axis.

A:

Q: Find the area of the region bounded by the parabola y = -x² + 4x - 3 and | its tangent lines at the…

A: We have to find the area of the region.

Q: 1. Find the area between the curves x2-y 9 and the line y 2x-6 %3D

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Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

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Q: 3. Find the area bounded by the curve y 4sin(2x), the x-axis, and the lines x = 0 and x =

A: We have to find the area bounded by the given curves. We will find the area by the help of…

Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y ?.

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Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

A:

Q: 1. Find the area bounded by the curves between the curve y=1+x and the line y-1 x

A: area between curve

Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

Q: 3 2. Find the area bounded by the two curves y = x³- 6x² + 8x and y = x² - 4x.

A:

Q: Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by…

A: To graph the function, solve the given equation for y. Since the region is in the first quadrant,…

Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

Q: Compute the area bounded by the curve y = x2 + 3, the x-axis and the ordinates x = 1; = 4.

A:

Q: 4 Find the area bounded by the curve y = the x - axis, and the vertical lines x = -2 x²+4 and x = 2.

A:

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.