The diagram below shows the curves y=sin x and y=cos x , and a region bounded by these curves and the x-axis (x is in radians). Find the area of the indicated (orange) region. Show and explain your work. Provide an exact answer, using symbols such as or T, as needed.

Q: Find the area of the region outside the circle r = √3 and inside the circle r=2 cos∝.

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Q: Find the area of the region inside: r = 5 sin 0 but outside: r = 1.

A: We will use double integration to solve this

Q: Find the area of the region that lies inside both curves. r = sin(20), r = cos(20)

A: Consider the polar curves:  r=sin2θ,r=cos2θSolve for θ:sin2θ=cos2θ2θ=π4θ=π8 There are 8 loops for…

Q: Help please

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Q: Find the area of the region inside r 8 sin 0 but outside r = 4.

A: Given. r = 8sin a r = 4 We need to calculate the area between the 2 curves

Q: Find the area of the shaded region. r = 6+5 cos

A: Introduction: The formula of the area inside the curve r=f(θ) is given by, A=∬rdrdθ Where limit of…

Q: Sketch the curve and find the area that the curve encloses. r = 3 cos 50

A: The solution for the above question is as shown below.

Q: sketch and find the area of the region enclosed by the graph of the equation r=3 cos Θ....

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Q: Find the area of the region enclosed by the inner loop of the curve. r = 2 + 4 sin ?

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Q: Sketch the region that lies inside the circle r = 6 cos 0 and outside the circle r = 3. Th ind the…

A: Given region lies inside the circle  And outside the circle

Q: Find the area that the curve encloses and then sketch it. r= 10 cos(36e) y 5 -5 -5 - to -5

A: Answer

Q: Find the area of the region that is inside the circle r = sin θ and outside the cardioid r = 1 −cos…

A: Please see the below picture for detailed solution.

Q: Find the area of the region inside the circle r = 4 cos θ and outside the circle r = 2.

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Q: Find the area of the region inside: r = 6 sin 0 but outside: r = 2

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Q: Let R be the region bounded by the rose curve, r = 6 cos(60) as shown in the diagram below. Find the…

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Q: 8. Graph the curve and find the area that it enclosed: r = 2 cos(0).

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Q: Determine the area of the given region. y = sin x for 0 to pi/3

A: Given:

Q: Find the area of the region. Interior of r = 6 sin 0

A: A detailed solution is given below.

Q: Let R be the region bounded by the rose curve, r = 8 cos(70) as shown in the diagram below. Find the…

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Q: Find the area of the region. Interior of r = 6 sin e

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Q: 8) Find the area of the shaded region : y = sec? x 2+ 1 y = cos X 4

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the area between the curve r = sin (3θ) and the first and second quadrant.  Graph.

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Q: Find the area of the shaded region shown in the graph. y= 15 sin x 15 y= 15 cos x

A: Integration gives the function whose derivative is given. Integration is nothing but adding slices…

Q: r = sin 40

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Q: Find the area of the following shaded region. y = 1 y = cosx

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Q: Find the area of the region that lies inside the curve r = 10 cos 0 and outside the curve r = 5,…

A: Given curve r=10 cos θ, r=5

Q: Find the area of the region inside 2 petals of the rose r = sin 80

A: Solution :-

Q: Find the area of the described region. region enclosed by r = 16 sin(0)

A: Find the area

Q: Find the area of the shaded region in the diagram given below. y = sin(2r) 6 y = cos(x)

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Q: 8) Find the area of the shaded region: y = sec? x 1- y = cos x 4

A: Consider the formula for the area between the curves. From the given graph, find f (x), g (x), a and…

Q: y = sin x 2

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Q: 18. sec² x 4 y = 4 cos² x

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Q: Find the area of the shaded region shown in the graph. y = 12 sin x y= 12 cos x .

A: Given, The two curves y=12sinx and y=12cosx intersect atx=π2 in x∈(0,π)

Q: Find the area of the region bounded by the curve given by the equation r = (1 + cos x ). O A) 87 O…

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Q: Find the area of the shaded region shown in the graph. Ay y = 27 sin x 27 y= 27 cos x

A: Solution :-

Q: Find the area of the region inside: r = 7 sin 0 but outside: r = 1

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Q: Graph the curve and find the area that it encloses. r = 2- cos e

A: Given: r=2-cosθ

Q: Find the area of the region enclosed by one loop of the curve. r = sin(40)

A: This question is about application integral

Q: Find the area of the region inside one leaf of the three-leaved rose r= 4 cos 30.

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Q: The area enclosed by the circler= = sin 0 is given by 2x esin 0 A = f" Sr dr d0.

A: Given that  The area enclosed by the circle r=sintheta is given

Q: Find the area of the region inside: r 8 sin 0 but outside: r = 1

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Q: r=2a+acos 20 A r=sin 20

A: The polar curves do not intersect at any point. The area between the curves is the shaded region.

Q: Find the area of the region enclosed by one loop of the curve. r = 8 sin(50)

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Q: Find the area between the two curves in the following figure: r=2a+acos 20 r =sin 20 For a = 14

A: Given: r=2a+acos2θr=sin2θa=14

Q: Find the area of the region inside: r = 7 sin 0 but outside: r = 3

A: I am going to solve the given problem by using some simple  calculus to get the required result.

Q: Find the area of the region inside: r 10 sin 0 but outside: r = 1

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Q: Find the area of the region that lies inside both curves. r = (3)1/2 cos(θ),    r = sin(θ)

A: Calculate the value for intersection points and the values for theta where both the value for both…

Q: Find the area of the region enclosed by one loop of the curve. r = sin(10θ)

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Q: 7. r a sin 3 e

A: Explanation: Given that,  r=asin3θ  Here we will put  r=0sin3θ=0⇒3θ=0 or π⇒θ=0 or π3