a. Find the intersection points of the curves y=x2+3x,    y=2−4x2:   x1=     ;   x2=      x1

Q: The area bounded by y = e*, y = 2, and the y– axis is equal to

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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: What is the area of restricted region between the curves y = -2x2, 2 and x -axis? 7/12 13/12 O 1/12…

A: solution of the given problem is below...

Q: Find the area bounded by the parabola x = y² + 2 and the line y = x – 8. 11 -2 3.

A: We have to find out the area bounded by the two curves

Q: find the area bounded by the given curves. y = 8x^3 + 1 and y = 8x + 1 square units

A:

Q: Find the area of the region bounded by the parabola y² = 2x2 and the line y = x - 5. 16 17 18 19…

A: Given: y2=2x-2 and y=x-5 Now find the point of intersection between the given curves. y2=2x-2 ;…

Q: Find the area enclosed by the xx-axis and the curve x=t^3+1x=t3+1, y= 2t-t^2y=2t−t2.

A: Given curves are x=t3+1, y=2t-t2.

Q: The area bounded by the curve x = 5y + 8, the y-axis and the abscissas y = 0 and %3D y = 2 is

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Q: 3. Find the area of the region bounded by the parabola y? = 2x – x and the line y = x – 5 by taking…

A: We have equation of parabola  y2=2x-xy2=x                                                     ……(1)…

Q: 9. Find in two ways the area bounded by the parabola y = x², the y-axis, and the lines y = 1, y= 4.

A: Given,  The parabola y = x2  We have to find the area bounded by the parabola, y-axis and the lines…

Q: Consider the area formed by the curves f(x) = x² + 1, y = x°, and the y axis in the first quadrant

A: The area between the curves y=x3 and fx=x2+1 on interval 1.46557…, 2.46557…:   The area between…

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 bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: d) Find the volume of the solid formed when the area bounded by the curve y = 3x – x? and the lines…

A: The volume of the solid generated by the revolution of the area bounded by the curve y=f(x), 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: The area bounded by the curve y2=12x and the line x=3 is revolved about the line x=3. What is the…

A: The correct answer is option C. Given  y2=12x and equation of line x=3 The point at which the line…

Q: The area bounded by the curve x = 4y + 7, the y-axis and the abscissas Y = 0 and y = 2 is 11 22 18…

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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: 4. Y = x2 (x-3) and y?+ 8y -16x + 48 = 0

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Q: The area which is enclosed by the curve x2 – 10x + 4y + y? = 196 is O 12n 15n О 14п 144n O 225n

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Q: Find the area enclosed by the given curves. y = x°, y = 4x 4. O 16 2 8.

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Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: Find the area bounded by the curve y²=4x, the lines x=1 and x=4. 56 (A) - sq . units 3 B 24 sq .…

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Q: Find the area bounded by the given curves. v = 6x² – 16x – 7 and y = 3x2 + 2x – 22 | square units

A: Given curves are: y=6x2-16x-7y=3x2+2x-22

Q: Find in two ways the area bounded by the parabola y=x^2, the y-axis, and the lines y=1, y=4

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Q: Find the area enclosed by the given curves. y = x3, y = 4x O 4 O 2 8 O 16

A: topic - area enclosed by curves

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: First we draw the graph,

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

A:

Q: 11. Find the area within the curves y 25-x', 256x=3y², and 16y = 9x². A. 37.26 units? B. 37.62…

A: Given the curves  y=25-x2 ,256x= 3y2 , and 16y=9y2 Determine the area within the given curves

Q: 30. Find the area bounded by the curve 5y²=16x and the curve y²=8x-24. A. 36 B. 25 C. 16 D. 14

A: Topic = Area

Q: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: Find the area enclosed by the curve x = t2 − 3t, y = Square root of t

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Q: Find the area bounded by the curves y = 6 – x² and y = 8 – 3x. 1 а) 1 b) c) d) 12 e) 12 -/3

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Q: Find the area between the curves. 4x y3e 8. x= 0, x= 3, y= 2 e y=e+ e

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Q: Find the area bounded by the curve y? 4x and the lines x=1 and x=4.

A: Area bounded by a curve y=f(x) and the lines x=a and x=b is given by, A=∫abf(x)dx  We know, ∫xndx=…

Q: Find the area bounded by the given curves. y = 2x – x², y = 2x – 4 - Write your answer in the form…

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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 area between the curves y = e and y = ex (shown below) from x = 0 to x = 2. (Leave the…

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Q: ind the area between the curves.   x = -2, x = 1, y = 2 x 2 + 4, y = 0

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Q: Question 2 Area bounded by the curves y=e*, y=e", x=0 and x=In2 (А) 604/9 (В) 304/14 C) 502/9 304/7

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Q: Find the area enclosed by the given curves. y = 2x - x 2, y = 2x - 4 O 32 O 34

A: The given question can be solved as shown in step 2.

Q: 12. Calculate the area of the segment cut from the curve y = x (3-x) by the line y = x. A. 5/3 sq.…

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Q: 6. What is the area bounded by the curve x²-9y and the line y+1=0. A. 6 C. 4 B. 5 D. 3

A: Given: x2=-9yy+1=0

Q: Find the area bounded by the parabola y2= 4x, the x – axis and the lines x=1 and x=3.

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Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: Find the enclosed area by the curve with equation y = x² - 9 and the X-axis in the region [−1, 2] 24…

A: In this question, we want to evaluate the area of the region enclosed by the curves y=x2-9 and X-…

Q: Find the area in square units bounded 1) y2 = 4x, x=0 to x= 4

A: Area Bounded by the curves :   If x=f(y) and x= g(y) be two continuous function on a,b and f(y)…

Q: Find the area bounded by the given curves. y = x², y = 2x² - 3x A. 9.0 sq. units B. 40 so units CAF

A: We have to find 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.