Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using: a. Rectangular method (n=5)

Q: Q3 Shade the area of the region bounded by, x² + y² p Hence, find the area of the specified region…

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Q: Find the area A of the region between y = 4x2 + 10 and y = 2x + 7 over the interval [-3, 2].

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Q: 3 Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

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Q: y = 2 – x2 ; y =-x

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

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Q: Q2/ Find the area of a region bounded by the curve f(x) = 8x' and x-axis and the two lines x=1, x=3.…

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Q: Shade the area of the region bounded by, x² + y2 < 7² and |x| + |y| 2 7 Hence, find the area of the…

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Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| and y =…

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Solve the area bounded by y3 + 10y + 5 = x², the y-axis and the lines y=0 and y=3 *

A: Given:  The boundary curve1. y3+10y+5 = x2  OR x = ±y3+10y+5 2. y=03. y=34. x=0 y-axisThe given…

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

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Q: Find the area of the curve y = x° – 2x – 3 between x =- 1 to x = 3.

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

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

A: We have to compute the area between the given curves using the double integration method by first…

Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

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

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Q: Find the area of the region bounded by y = xInx and the x-axis between x=1 and x = e

A: Using formula of Area Under The Curve.

Q: The area of region bounded by the parab y = 2x – 4 is

A: Introduction: Integration is a method of bringing separate parts to form a whole. We find a function…

Q: Find the area bounded by the ff. curve and line: y = xe^– x , the x-axis and the maximum ordinate

A: The curve y=xe-x, we have to find the area bounded by the curve, the x-axis and the maximum…

Q: Determine the area bounded by: y2-12y-8x+28=0; and x2-4x+4y-20=0

A: The given equations: This can be rewritten as, To find the area bounded by the above equations:…

Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

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Q: Find the area bounded by the ff. curves and lines: a. y = xe^–x , the x-axis and the maximum…

A: To find the are bounded by the curves and lines: (a) y=xe-x, the x-axis and the maximum ordinate.

Q: Find the area bounded by y = X = 0, y = 0, and x = 3. V49-16x2

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Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

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

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Q: Find the area bounded by the curves y = 3e2x and y = 3e-x and the ordinates at x = 1 and x = = 2.

A: The region is

Q: Find the area of the region under the curve y = 6x² + 4x + 5 from x = -1 to x = 2.

A: Solve the following

Q: Find the area bounded by y² = 4a(y-x), y² = 2a(x+2y-3a) and the x-axis

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Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: The area of the region bounded by the curve y= x3−3x2−x+3 and y=0 is

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Q: Find the area of the region bounded to the right by x = y + 2 and to the left by x = y². 543-2 1…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: 3 Find the area of the region bounded by 2x = y²+1 and the y-axis using the horizontal strip.

A: The given region is bounded by 2x=3y2+1 and the y-axis.

Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

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Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

Q: Use the method of partial fractions to find the area bounded by the curve y

A: The given function y -y = 2x-8x2-5x+6y = 2x-8x2-2x-3x+6y = 2x-8x(x-2)-3(x-2)y = 2x-8x-2x-3Using…

Q: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

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Q: The area of the region bounded by the curves 8x =y° and 8x = 2y+y2 -2y is

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Q: Find the area between the curve y = 2x² + 4x-6 and the x-axis from x = -2 to x= 3. %3D %3D %3D

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Q: Find the area of the region bounded by the curves y² - 4x = 5 and 4x + 3y = −1

A: We can find the area of the region between the two curves using the double integration method. We…

Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

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Q: Find the area between the curve f(x) = −3x^2 + 3 and the x-axis over the interval [−1, 2].

A: Answer and explanation is given below

Q: Find the area bounded by the two curves f(x) = x2 – 8x + 8 and g(x) = - x² + 6x – 8, and the two…

A: The given two curves:fx=x2-8x+8 and gx=-x2+6x-8and the two vertical lines are x=3 and x=4.We need to…

Q: find the area bounded by y = (2x - 3) / (x^2 + 4), the coordinate axes and the minimum ordinate

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Q: Find the area of the region bounded by one loop of the curve x2 y*(1 – y²)

A: Given:          x2=y41-y2         x=±y41-y2         x=y21-y2 The graph is symmetric about the…

Q: Find the area of the region bounded by the parabola y2 = 2x-2 and the line y = x-5 using (a)…

A: We will find out the required area.

Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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Q: f the region bounded by the curves y = x3-8x2

A: The region bounded by the curves are y=x3-8x2+20x , y=-x2+8x…

Q: Solve the area bounded by y³+y²+10 = (x+1)², the lines y=−2 and y=2 *

A: The given problem is to find the area bounded by given region and between the given lines y=-2 and…

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.