4. (Areas of Plane Regions). Use Wa to plot the curve 2/3 + y?/3 = 42/3 (+ z|2/3 + ly|²/3 = 42/3) %3D (an astroid), and then find the area of the region it encloses (think what trigonometric substitution you can use once you'll get a definite integral whose value is equal to the area in question).

Q: 6. Determine the area of the region (a) outside the cardioid r = 1 + sin 0 and inside the circle r =…

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Q: Find the area of the region that lies inside both curves. r = 2 + cos(0), r = 2 - cos(0)

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Q: Find the area of the region that lies inside the curve r = 1 + sin 0 and inside the curve r = 1.

A: Given: The curves  r=1+sinθ and  r=1. To Find:  Area of the region that lies inside both of the…

Q: Sketch the region that lies between the curves y = 4 sin(x) and y = 3 cos(x) from x = 0 to x = 0.37.…

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Q: Find the area of the region that lies inside both curves

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Q: 7) Find the area of the region that lies inside both of r = 1 - cos 0 r = 1 - cos 0 the curves and

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Q: 9. Find the area of the region that lies inside both curves * r = 2 sin(0) and r = 2 cos(0) O -1 27…

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Q: Find the area of the region bounded between the curves y = sin(x), y = cos(x) on the following 4 -27…

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Q: ine the slope of the tangent line at the non-pole point on C2 which inter he integral that gives the…

A: Sol

Q: 10) Find the area of the region that is bounded by the given curve and lies in the specified sector.…

A: In the given question we have to find the area of the region that is bounded by the curve r=tanθ and…

Q: 8. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and…

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Q: 5. Using iterated integrals, find the smaller area cut form the circle x² + y' = 16 and the line y…

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Q: 2. Find the area of the region that lies inside both curves r = 4 sin(0) and r = 4 cos(0) ● 플 +1 2T…

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Q: 2. Find the area of the region that lies inside both curves * r = 4 sin(0) %3D and r = 4 cos(0) 2л -…

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Q: Find the area of the region enclosed between y = 2 sin(x) and y = 4 cos(x) from x = 0 to x = 0.6.…

A: To Determine: Find the area of the region enclosed between :

Q: Find the area of the shaded region 14 12 bounded above by y = 2, bounded below by y = cos(x) + 1,…

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Q: Area inside the circle r = 3 cos 0 and outside the cardiod r = 1+ cos 0

A: The region which is inside the circle r=3 cos θ and outside the cardioid r=1+cos θ is:

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/…

A: The curve is given as y=cos2x The objective is to find the area of the shaded part.

Q: 4) Find the area of the region bounded by the given curves. a) y = sin(x) cos(x) and y = sin(x) , 0…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: 1 Find the area onclosed by the Curve r=4-3 sin 0.

A: Area

Q: 4. a) calculate the area of the area bounded by the Curves TI y=Sin 2x and y sin 2x, OSX<

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Q: d the area of the region bounded by the curves: y = cos(nx) and y = -1 + 4x²

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Q: 2. Find the total area of the region between the curves y = sinx and y = cosx for 0<xs 37 2

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Q: Find the area between y,= 2 sin x and y = 5 cos x over the interval [0, 7]. Sketch the curves if…

A: Topic:-  application of integration

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 2+…

A: By sketching graph

Q: 4. Set up the integral for the area of the surface obtained by rotating the curve y = e-x -1 < x< 1.…

A: Given: The area of the surface obtained by rotating the curve y=e-x2  and -1≤x≤1 we have to…

Q: 5. Find the area of the region R that lies outside the curver=2 and inside the curve r = 4 sin 0

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Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 6 – 6…

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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:  We have given two curves r=10 cos θ, r=5 To Find:  Area of the region that lies inside the…

Q: Find the area of the region enclosed between y 3 sin(x) and y = 2 cos(x) from x = 0 to x = 0.6T.…

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Q: 1) Find the area of the region bounded by the curves: x=2y2 and x=16+y2 2) Find the area of the…

A: Important points: 1. First we will draw both the parabolas by finding their vertex. 2. Then we will…

Q: Find the area of the region bounded by the curve r = 8 cos 2θ.

A: We need to find the area of the region bounded by the curve r = 8 cos 2θ. Let us first plot the…

Q: Calculate the area between the curves r2=16 sin 2Ɵ and r2=16 cos 2Ɵ.show by drawing.

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Q: 4. Sketch the curve of r2 = cos 20 and find the area that encloses it. Show your complete solution.

A: In polar coordinates,  r=x2+y2, θ=tan-1yx Converting the polar equation to cartesian coordinate…

Q: 2. Find the area of the region that lies inside both curves = 4 sin(0) and r = 4 cos(0) O +1 2T - 1…

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Q: 9. Find the area of the region between y = sin 0 and y = sin e , between 0 = 0 ande = n/2. %3D

A: To find the area of the region between,  y = sin3 θ  and y = sin θ Between θ = 0 and θ = π/2 The…

Q: 7. Find the area of the region cut from the first quadrant by the curve r = 2(2 sin 20)¹/2

A: Solution :

Q: 1. Sketch the curves 4x + y? = 12 and y = x and shade the area bounded between them. Then set up an…

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Q: Sketch the region enclosed by the given curves and solve for the area. y = 2 cos(4x),    y = 2…

A: The given two function are y = 2cos (4x) and y = 2sin (8x).The region enclosed by the curve y = 2cos…

Q: 3. Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis…

A: Follow the procedure given below.

Q: 2. Find the area of the region that lies inside both curves * r = 4 sin(0) and = 4 cos(0) 2л — 1 ●…

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Q: 8) Find the area of the region that lies inside both of the curves r = 1 + cos 0 and r = 1 - cos 0…

A: We have to find the area between the given polar curves. The graph of these curves is as shown…

Q: (4) Find the area of the region bounded by the curves y = sinx, y = cos I, I = T x = 3π/2. You will…

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Q: Find the area between y= 2 sin x and y = 5 cos x over the interval [0, 7]. Sketch the curves if i…

A: Given: y=2sinx y=5cosx

Q: Find the area of the region enclosed between y = 2 sin(x) and y = 2 cos(x) from x = 0 to x = 0.37.…

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Q: 4 / Find the area of the region enclosed between the curves y%3= cos 2x, y=0, x-TT/4, x- TT/2 ? ans/…

A: we allowed providing one solution at a time. Please upload the rest questions seprately.   Question…

Q: r = 3 cos 0

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Q: Find the area of the region bounded by the given pair of curves. Area inside the circle r = 3 cos 0…

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Q: Find the the region that lies inside the area OF Curve r- sin o and outside the curve r: 1+ sin 0.

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Q: r = 2 + sin 0, r= 3 sin 0

A: For given  r = 3sin(θ) r =2+sinθ Area is calculated as shown below