2. Find the area outside the inner and inside outer loop of the limacon r = 4 sin 0 - 2 101

Q: Evaluate the integral. ∫Sin3 θ Cos 4θ  dθ

A: We have given;

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Q: Find the area of the shaded region of the graph of r=1+sin (0)

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Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; 1-cos20…

A:

Q: To evaluate the integral sin ³0cos (A) sin²0=1-cos²0 1-cos20 B sin ²0 2 sin20 sin cose 2 1+ cos20…

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A: Given :   I1=∫01.2xsinex3dx

Q: Use

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Q: Evaluate the integral. sin COs 503 502 502 sin 50 1. cos d0 3D 502 502

A:

Q: 4. Find the area common to the circler=3 cos 0 and the cardiod r=1+ cos0.

A: Find points of intersection and solve the given problem. A detailed solution is given below.

Q: Find the area between the inner and outer ovals of r = 4(1+sine

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Q: Find the area lying outside r = 4 cos 0 and inside r = 2+2 cos 0.

A:

Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: Evaluate the integral | : sin 20 do 3+ cos 20 using the substitution u = 3+ cos 20. sin 20 Op 3+ cos…

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Q: 8. Find the area enclosed by 1 leaf of r=sin30

A: Let's find.

Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

A:

Q: The area (number) inside the one loop of r^2=4 sin2 theta is

A: We have to find the area enclosed in the loop of r2=4sin(2θ)

Q: b) Find the common area between r= 4 cos (0) and %3D r=2 sin (0).

A:

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

A:

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: 17. Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the…

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Q: Find the area of the shaded region of the graph of r=1+sin(0)

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Q: To evaluate the integral [sin³0cos 60d0 by trigonometric transformation, we use the identity:…

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Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: 2. Find the area enclosed by T = @ cos 30-

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Q: 1- Find the area under one arch of y = cos3 x

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Q: Look for the smaller loop of the limacon r = a(1+2 cos 0) and solve for its area.

A:

Q: To evaluate the integral sin³0cosº0de by trigonometric transformation, we use the identity; 1- cos20…

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Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: Calculate the area between the curves ² = 16 sin 20 and ²: = 16 cos 20 .Show by drawing

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Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: Evaluate the integral / sin 50 do 2+ cos 50 using the substitution u = 2+ cos 50. sin 50 do 2+ cos…

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Q: find the area of the limacon: r = 2 + sinx

A: To Determine: Find the area of the limacon:

Q: what is the integral of cos(6x)xsin(sin(6x)) from 0 to pi/12

A: Given,

Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

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Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: Derve the Jrmula Cosh 2. Find dy Sor Sin ソー X-/ xp

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Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 8 O 6 None of them O 2 O 4 O

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Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

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Q: Sketch the graphr=6-6 cos 0 and find the area enclosed by r=6-6 cos 0.

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