Determine the area of the region enclosed by y =r and y = I. O 9 O 46/3 2/3 O 1/3 O 142/9 O 142/3 46/9 O 32/3 3.

Q: sketch the region enclosed by the carves and find its area X Sy + 1a = .....

A: The detailed solution is explained in steps 2 and 3.  First we have to sketch the curves and then…

Q: Find the area of the region bounded above by y = x + 2 and below by y => X 542 1 1 2 3 4 5 -2 -3 O O…

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Q: Find the area of the region bounded by y = x and y = x O 1/2 O 1/6 O 1/3 O None of these

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Q: 41. S = {(x, y) |x> 1, 0< y sey 41-46 Sketch the region and find its area (if the area is finite).

A: The given region is: S= (x, y)| x≥1,  0≤y≤e-x

Q: Find the area, square unit, to the nearest hundredth, that satisfies the given condition. The region…

A: Obtain the area of the region under the standard normal curve that lie to the right of z is 1.42.…

Q: Find the area enclosed by the cardioid r = a(1 + cos θ), where a &gt; 0.

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Q: Let R be the annular region Tying between the two circles x + y- x? + y? = 5. Evaluate the integral…

A: The solution follows as :

Q: Find the area of the region. x- 5 y 1.0 0.8 0.6 0.4 0.2 5 10 15 20 25

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Q: Find the area bounded by the given curves. x = 0, x = 1, y = x² + 6, y = x² + 2 Select one: O A. 16…

A: Please refer the attached image for complete solution.

Q: Find the area bounded by ? = (1− ? ² )² and ? = 0. Please draw the figure to show the bounded…

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Q: 3) Find the area of the region enclosed by the cardioid r=1-cos®

A: See the details solution in below

Q: 5. Find the area of the region enclosed by y 1 1 y = x, y = x, and x > 0.

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Q: Give area of the region enclosed by y and y = 0 from x = 1 to x = 3. 2 A. 2 В. 3.4 С. 1.5 D. 1

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Q: Find the area of the region enclosed by x - y? = 0 and x + 2y? = 3 25 - O A) 2 O B) 3 OC) 5 O D) 1 O…

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Q: 7) Find the area of the region enclosed by the cardioid r² = 4 cos 20.

A: To find the area of the region enclosed by the cardioid r2=4 cos 2θ.

Q: Consider the following shaded region. YA y=ax - x? y=bx Find the area S of this region if a = 4, b =…

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Q: Consider the following shaded region. y=ax – x? y=bx Find the area S of this region if a = 4, b = 2.…

A: Firstly we will find the point of intersection from graph as shown below and then find area of…

Q: Find the area of the region bounded above y = e, bounded below by y = x, and bound on the sides by x…

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Q: Compute the area of the shaded region. y=-x+4 p+X =Á O 2 16 8. 32

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Q: x? + y? = 4 and x? + y? = 4x Compute the area bounded by

A: The given equations  are

Q: 5. Find the area between x = y + 1, y = Vx and x = 0.

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Q: y = x², y = 0, x = 1, and x = √5

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Q: Determine the area of the region bounded by x = y? – y – 6 and x = 2y + 4. O 21.33 O 7.50 O 10.67 O…

A: To determine the area of the region bounded by x = y2 - y - 6 and x = 2y + 4.

Q: BY GI Evaluate, F(r) C of the region / I,F = [y, -x

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Q: Determine the area of the given region. y = 4x(1-x) A 10 A 7 6- 4 2 0.25 0.5 0.76 1.26 1.5 1.76 2…

A: Given, a= 0 b= 1 f(x)= 4x(1-x)= 4x-4x²

Q: 4. Find the area of the region enclosed by y = –x² + 6, y = x, y = 5x, and x 0.

A: Area bounded by the region y=-x2+6, y=x and y=5xFirst we sketch the region

Q: Sketch and find the area of the region lies inside the cardioid (r = 1+ cose) and outside the circle…

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Q: Find the area bounded by y =e*, x=0, y = 0, and x= 2.

A: topic - area bounded by curves

Q: Determine the area of the region bounded by y = y = 2x and x =4. 6.45 57.17 O 1.57 O 23.91 O 7.50…

A: We have to determine the area of the region bounded by the curves y=8x, y=2x and the line x=4. First…

Q: 2. Find the area of the region enclosed by æ + y? = 0 and ¤+3y² = 2.

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Q: 0 Figure A y = x³ y = √√x X

A: Given

Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1? O…

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Q: Sketch the region enclosed by the given curves and find the area. x = 2y ² ,  x = 4 + y

A: Sketch the region and integrate in y variable.

Q: Evaluate xy dA R over the region R enclosed by y = x/2,y = VI, I = 2 and r = 4.

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Q: What is the area of the greern region. B as an integral? o ) dr 1 9 (z) dz of) dz + 1(1) dz What is…

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Q: 5. Find the area of the region enclosed by y = =, y = x, Y = 7x, and x > 0.

A: Ans: 0.69315 sq.unit

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: Find the area of the region described in the following The region bounded by y = 24 Vx and y = 3x?

A: Given, y=24x &amp; y=3x2 To find limits of x we have, y=24x =3x2⇒24x =3x2⇒8x=x2 Now squaring on the…

Q: Let R be the region given by 0 SzS a? + y? , a² + y? <3. Evaluate (x + 2)dV.

A: The given integral is ∭Rx+2dV where R is the region given by 0≤z≤x2+y2, x2+y2≤3. We know that the…

Q: 6dA, where R is the region given by { (x,y,z): 1sx²+y?s16, x²+y²szs16-x²-y2}. Evaluate

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Q: 2. Find the area of the region bounded by y = VI and y = r.

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Q: etch the region enclosed by y = x²y = √√x,x = 0,x = 1 and find its area.

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Q: Sketch the region enclosed by ?=5?y=5x and ?=3?2y=3x2. Decide whether to integrate with respect to…

A: Given: y=5x, y=3x^2

Q: Which of the following shaded regions has an area equal to In 2? y = 1/x y = 1/r A. 1 3/2 2 2 В. 4 y…

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Q: Find the area between y = In x and the x-axis from x = 1 to x = 3. 3 In 3 – 3 In 3 3 In 3 + (-2) OD.

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Q: Find the area of the region enclosed by x - y? = 0 and x+ 2y2 = 3 2- O A) 2 O B) 4 C) 3 O D) 1

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Q: Find the area of the region enclosed by x = y' and x Vy- 6. Answer:

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Q: Determine the value of z such that the area between 0 and z is 0.4564 and z is positive. Oz = 1.81…

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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.