2) a- Set up inside r=3+3 Sint and the area outside (=3. b-Set up the area inside r= 3+3 sino and inside r3.

Q: 21. Given the integral [ cot³x csc ³x dx. If u = cscx, then the integral can be re - written as:

A:

Q: Find the total area between r = 4 sin(0) and r = 7 sin(40). %3D

A: Double integral is used to integrate the function of two variables over two-dimensional region.…

Q: Find the area outside "r^2=9cos(2theta)" and inside "r=2-cos(theta)"

A:

Q: Find the area inside one leaf of the three-leaved rose r = cos(30), as scen here: -0.4 -0.2 0.2 0.4…

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Q: Use trigonometric substitution to find or evaluate the integral

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Q: Find the area that is shared by both cardioids r = 1 - cos(theta) and r = 1 + cos(theta).

A: Consider the region that is shared by both cardioids r = 1 - cos(theta) and r = 1 + cos(theta):

Q: Q4) Find the shared area between the two cardlold r=1+sin@ and r%3D1-sin0

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Q: Find the area of Sin(x) over the interval of (0, pi)

A: Area of Sin(x) over the interval of (0, pi) is given by:

Q: consider limaçon r = 2 + 3 cos θ and the circle r = 2 cos θ in one polar plane.   - Set up the…

A: Plot the curves for the given limacon and the circle. The shaded region represents the area inside…

Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin .

A: This is a problem related to area of the polar curve. based on the graph of limacon curve we will…

Q: 2- Find the area f the negion cut from the trst quadrant by the regson r= l+ Sino?

A: From the given problem:   r=1+sinθ   Given first quadrant it means:   θ→0 to π2r→0 to 1+sinθ   Now…

Q: - Find the area of the negion that inside (i=3sin@) eind also In side (rz = + sin@) ?

A: To find the area of the region inside r1=3sinθ and inside r2=1+sinθ

Q: Q4/ Compute the area outside the cardioid r = 4-4 sin(0) and inside the circle r=2.

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Q: Find the area inside r=1+sin θ and outside r=3sin θ.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the total area between r = 4 sin(8) and r = 7 sin(40). %3D %3D

A: Given curves are r=sinθ, r=7sin4θ To find : area between the curves

Q: Determine the area of the right half of the cardioid formed by r = 7+6 sin 0 14 12 10 8 6 2 -2 -4…

A: Explained below

Q: Find the area of the region outside r = 8+ 8 sin 0, but inside r = 24 sin 0.

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Q: Find the area bounded by the parabolic arc Vx + Jy = 7 and the chord joining (9, 16) and (16,9).

A: Topic = Application of integration  Area = 7/3

Q: Find the area enclosed by r = √2 sin 0 and r² = cos 20.

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Q: 4. Find the area enclosed by: a. y= sin(x) and y= cos(x), x 0, x =" and the y-axis. 2

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Q: 5. Use trigonometric substitutions to evaluate the integral: I Væ(4 – #)dx.

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Q: the Area that lies inside r=3+2 sin 0 out side r=2 is 24.315 O -24.187 O 23.957 O 24.187 O -23.957

A: Solution:-

Q: Show that if k is a positive constant, then the area between the x-axis and one arch of the curve y…

A: y = sin kx cuts the x axis at y=0. Solve for x.

Q: 12. Find the area inside the cardioid defined by the equation r = 1-cose.

A: Equation of cardioid given is

Q: Find the area pebal r=4 sin C30) of one

A: Let's now plot the graph:

Q: Find the area between y = x + 11 and y = 3x + 2 between x O and x 2. %3D |3D Enter the exact answer

A: Given:       y=x+11       y=3x+2 over interval 0,2 The area between curves is the area between a…

Q: How is the area y > -1 converted by mapping w = iz ?

A: Given area y>-1 mapping is w=iz Let w=u+ivz=x+iv

Q: What is the area within the curve r2 = 16 cosϴ. Choices: 16, 32, 64, or 8.

A: Since area bounded by region is in +ve as well as -ve  So area is

Q: Find the area enclosed by r = 2 sin 30.

A:

Q: Find the area between y = 7 sin (x) and y = 7 cos (x) over the interval [0, π]. (Use decimal…

A: For the cartesian curves y1=f1(x) and y2=f2(x) where y2>y1 in the limit x=a to x=b, the area…

Q: Now, the area is given by I((6 - 6y2) – (6y2 – 6)] dy = dy.

A:

Q: Find the area enclosed by one "leaf" of the three-leaved rose: Bepaal die area wat deur 'n "blaar"…

A: Find the area enclosed by one leaf of r=4cos15θ such that -π30≤θ≤π30

Q: Find the area inside r = 2(cos 20- sin 2 0) and outside r 1 %3D

A: The area inside r2=2(cos2θ-sin2θ) and outside r=1 is:

Q: (b) By reffering to Figure 2, give an integral equal to each area. y A y = 2.x y = x² 4, A, х Figure…

A: Given

Q: (b) Suppose we wish to estimate the area 3 Vĩ dx 2 using the Trapezium rule.

A:

Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin 0.

A: Solution :-

Q: What is the area inside r=3cos theta and outside r=1+cos theta?

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Q: В. Determine the area that lies inside r = 3 + 2 sin 0 and outside r = 2. %3D r- 3+ 2 sin e 8 = 4 r=…

A:

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is -23.957 O -24.187 O 23.957 O 24.315 O 24.187 O…

A: We have r=3+2sinθ  , r=2 We find the point of intersection: 3+2sinθ=2⇒sinθ=-12⇒θ=sin-1-12⇒θ=7π6,…

Q: Find the area enclosed by r² = 4 sin 20.

A:

Q: Of the expressions w could be correctly I to compute the area ded by graph Y=10x- and line y=2x ?

A: Please refer to the image below

Q: The suitable substitution to evaluate the integral cot (2x) dx is sin (2x) O u= tan(2x) O u= csc(2x)…

A: Integral is given

Q: 4. Find the area enclosed by: a. y= sin(x) and y = cos(x), x= 0, x = and the y-axis.

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

Q: Calculate the area enclosed by r = 6 cos(3 0) for а) 67 b) О 2л 37 97 97 2

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Q: The area of the region enclosed by y = 8 +|cos x|, y=8, x = 7n and x = 187 is

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Q: Find the area of one leaf of the rose r = sin(15θ). Enter your answer in terms of π, do not use…

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Q: Find the area under one arch of the trochoid x 70-1 sin(0), y = 7–1 cos(0).

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Q: Find the area that it encloses. r = 2 − 2 sin(?)

A: To find: The area that encloses r = 2 − 2 sin(?). Graph: The polar curve  over the interval [0,2pi]…