Q3/ Find the area of the region that lies inside r=3 sin0 and outside r=2-sin0

Q: Sketch the region whose area is given by the definite integral. 36- х2 dx -6-

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Q: Sketch the curve, y=-x +9. Then, find the area between the curve and the x- - axis over the…

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Q: What is the area under the curve f(x) = sinx over the interval [0, pi/2]

A: First:                  Let's draw the graph of the curve f(x)=sin x  over the interval: [0, π2]…

Q: Find the area of the region bounded by: r = 5 – 3 sin 0

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Q: Find the area of the region bounded by the given curves. y = sin2(x),    y = sin3(x),    0 ≤ x ≤ π

A: Given: Find the area of the region bounded by the given curves. y = sin2(x), y = sin3(x),    0 ≤ x ≤…

Q: Use double integrals to find the area inside the curve r = 5sin(e)

A: The given curve is:

Q: Find the area of the region enclosed by one loop of the curve r = 4 sin(7theta)

A: Loop:- A curving or doubling of a line so as to form a closed or partly open curve within itself…

Q: Find the area of the region bounded by: r = 6 – 3 sin 0

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Q: What is the area of the region bounded by the graph of r = 4 sin 2θ

A: What is the area of the region bounded by the graph of r = 4 sin 2θ

Q: Find the area of the region bounded by the two curves x = sin2y and x = cos2y from y to y = n 8

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Q: Find the area of the shaded region. 21) 2- y = 2 2 sin(my

A: Since we are given with the multiple number of question and answered according to the guideline

Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: The given integral: ∫-π/4π/4tan x dx To sketch the area bounded by the given integral: Draw the…

Q: Sketch the region whose area is given by the definite integral. 8. x dx

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Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: The given integral is,

Q: Find the area under the curve y = 5xe- for x > 4. area =|| %3D

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

Q: Find the area bounded by y = 3x² - 3 and y = 3. Leave your answer %3D correct to 2 decimal places.

A: Given  y = 3x2  -3  and y = 3 To find : Area bounded.

Q: Find the area bounded by y =2x and y = 9x - x2. Sketch the region.

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Q: how to find  Find the area of the region enclosed by one loop of the curve. r = sin(4θ)

A: The given curve is r= sin4thetaArea of the curve enclosed in the first loop is,

Q: Find the area of the region which is bounded by y = sin x - 3, y = 3x, y-axis and x = 2. Leave your…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the area bounded by y = sin(x) and y = sin*(x) from 0 < x <.

A: Given,             y=sinx , y=sin4x from 0≤x≤π2To find : Find the area bounded by the curves.

Q: y (0, 3) y = 1 - sin (x - T/2)

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Q: 2- Region enclosed by the cardiaid (r=\- Sin@)in 1-st quadrant.

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Q: Find the area of the region cut from the first quadrant by the curve r = 2(2 - sin 2u)^(1/2).

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Q: Determine the area of the region bounded by y= x^2 +2 and y= sinx where x = 1 and x = 2

A: Given: Equation of curves:

Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 3. Leave your…

A: Area bounded by the given curves :If f(x) and g(x) be two continuous function on a,b and f(x) ≥g(x)…

Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: Therefore, the value of the integral is 0.23286.

Q: Find the area of the region that lies between the curves y = sec x and y = tan x from x = 0 to x =…

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Q: Find the area between the curve  y = −x2 + 3x − 2  and the x-axis from  x = 1 to x = 2.  (Give an…

A: Given: Find the area between the curve  y = −x2 + 3x − 2  and the x-axis from  x = 1 to x = 2.…

Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: Solution:Given  Let         I=∫-11tan-1xdxTo sketch th signed area represented by the integral and…

Q: Which integral requires more steps to find? Explain. Do not integrate. | sin° x dx OR sin°x cos x dx

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Q: Choose the integral that would find the area inside r =3 sin 0 and outside r = 2-sin 0. -1

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Q: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Calculate the area of the region bounded by the graph of f(0) = cose sine and the 0 - axis between 0…

A: Consider the given function: fθ=cosθsinθ Area of a function fx in interval a,b is given by:…

Q: y-3 sin() y- = 3x TEX y = 2 y

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Q: Find the area bounded by y = sin²(x) and y = sin5(x) from 0 < x<

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Q: Find the area of the region. y = sin 8x

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Q: Find the area bounded by y = 2x2 - 4 and y = 5. Leave your answer correct to 2 decimal places.…

A: This is area under the curve problem

Q: 10.4-#33

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Q: Sketch the region enclosed by the curves: y= x^2-1, y = 7-x^2. Then set up (but do not evaluate) the…

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Q: Find the area of the region that lies inside the first curve and outside the second curve. 3 - 3…

A: Let's find.

Q: Find the area bounded by y = sin²(x) and y = sin³(x) from < i< .

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Q: Find the area of the region bounded by: r = 5 – 4 sin 0

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Q: find the area of the region bounded by the graph y=cos^2x, y=sinxcosx , x=-pi/2 , x=pi/4

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Q: Find the area bounded by y = sin(x) and y = sin (x) from 0 <xs. %3D %3D

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Q: Find the area between y = 16 sin (x) and y = 16 cos (x) over the interval [0, n]. (Use decimal…

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Q: Find the area of the region enclosed by the curves y = 3 sinx and y = 3 sin 2x for 0sxsT.

A: Here we have to find the region enclosed by the curves y=3sinx and y=3sin2x .

Q: Find the area of the region enclosed by one loop of the curve. r=sin(8theta)

A: Draw the given curve as shown below.

Q: Find the intersection area between r = 3sinθ and r = 2 - sinθ curves.

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Q: Find the area of the region Cut from the Ist auadrant /2 r= 4(2-Sin 20) by the curve

A: Solve for the 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.