Total length of circle r= 9 sin theta as an integral in polar coordinates.

Q: Sketch the polar curve r = 2 − 2 cos(θ). can you please show how you found all the points necessary…

A: In the question it is asked to draw polar curve for function r=2-2cos(θ).

Q: Sketch the polar curve r = 2 sin 3θ by first sketching the graph of r as a function of θ in…

A:

Q: ermined the formula of area in polar coordinate with an exam

A:

Q: Find the points of horizontal tangency to the polar curve. r = a sin θ      0 ≤ θ < π, a > 0…

A: Calculation:The polar curve is r = a sin θ, where 0 ≤ θ < π and a > 0.In order to find the…

Q: Discuss the determined the formula of area in polar coordinate with an example ?

A:

Q: Find the area of the circle given by r = sin θ + cos θ. Check your result by converting the polar…

A:

Q: Interior of r = 9 – sin 0 (above the polar axis) -

A:

Q: Sketch the curve. Sketch the graph on the Cartesian plane first then on the polar grid.  r = 1 -…

A: graph on the Cartesian plane

Q: Find the area of the shaded region given the polar equations: r = sinx and r = cosx

A:

Q: Sketch the graph of the polar curve r = 1+3 sin 0 and calculate the area it encloses.

A: Given the polar curve is r=1+3sinθ.

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: The surface area of a solid obtained by revolving a polar curve r=f(θ), defined in the interval θ∈α,…

Q: Plot the curve of the polar function r(0) = 4 – 2 sin(40) And plot the polar circle r(0)=7 then find…

A:

Q: The origin in rectangular coordinates coincides with the............ in polar coordinates; the…

A: we have been given blank statement we have to fill it. Statement : The origin in rectangular…

Q: Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates.…

A:

Q: find the area of the surface formed by revolving the curve about the given line. Polar equation:…

A:

Q: The region shown at the right is bounded by portions of the y-axis, the line x = y, and the circles…

A: Given line is y=x  Inner circle radius=2 Outer radius=4

Q: sketch! Convert to polar coordin is the region in the first quadrant enclos

A:

Q: Given the polar curves: C1: r = 1+sinθ and C2: r = 3sinθ, I.   determine the curves' intersection…

A: Given: The polar curves: C1: r=1+sinθ and C2:r=3sinθ To find: I.   The curves intersection points in…

Q: 18. r = cos"/3' 19. r = cos 20, 0 = "/a

A: Given:- 18.  r= cos(π/3) ,θ = π  19.   r= cos(2θ) , θ = π/4 To find:- Find the slope of the tangent…

Q: Convert to polar coordinates with r,≥0 and 0≤theta<2

A: Given query is to find the the equivalent polar coordinates.

Q: Match the polar equation with the graphs labeled I-VI. Use the table to help you. r = 2 + 2 sin(0)…

A:

Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

A: We equate the two equation to find solutions.

Q: Do a complete analysis to determine the points of intersection of the polar curves r = 4 sin 0 and…

A: We need to find the points of intersection. So,              4sinθ=1+2sinθ⇒sinθ=12⇒θ=π6+2πn,…

Q: Transform polar function r = -9 cos(0) to rectangular coordinates and graph, label your graph clear…

A:

Q: A point has rectangular coordinates (2, – 2). Convert to polar coordinates, with r > 0 and 0 <0< 27.…

A: Given query is to find the polar coordinates.

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given:r=6 cosθInterval: 0≤θ≤π2S=2π∫αβ r sinθ r2+drdθ2  dθ

Q: duct z,z2 and the quotients 1 and (Express your answers in polar form.) Z2

A: We will solve the problem on complex numbers.

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given: The polar equation of the curve   r=eaθ  ,  0≤θ ≤ π2 , Axis of revoultion θ = π2   To…

Q: Area between two polar functions

A: In order to calculate the area between two polar curves, we’ll Find the points of intersection if…

Q: Convert the polar equation to rectangular form: r = 4 cos θ sin 2θ

A: Given that: r = 4 cos θ sin 2θ.

Q: P2: sketch in polar

A:

Q: a) Show that the polar equation r = a sin 0 + b cos 0, where ab # 0, represents a circle. Find its…

A: (a) The given polar equation of circle is - r=asinθ+bcosθ We need to find its center and radius . We…

Q: а. Use technology to graph these two polar functions, and then sketch the region R below. b. Find…

A: The area bounded by two polar curves 0≤r1θ≤r2θ , α≤θ≤β is given by 12∫αβr12-r22dθwe have given the…

Q: Convert the rectangular coordinates (square root2, square root2) into polar form. Express the angle…

A:

Q: Find the area enclosed by the polar r = 2 (1+sine) Curve

A:

Q: r = 3+2 cos 0

A:

Q: polar form to find the area

A:

Q: 4 Consider the point (5, –6) in rectangular coordinates. What is the radius in polar coordinates? (2…

A: Known fact: For a rectangular coordinate point x, y, the radius in corresponding polar coordinate is…

Q: Convert the point with Cartesian coordinates to polar coordinates. Enter exact values for r and 0,…

A:

Q: Calculate the area of the region inside the cardioidr = above the polar ray. Show by drawing. a(1 +…

A: Let A1 be the area inside the cordioid above polar ray 1  And A2 be the area inside the cordioid…

Q: Use a graphing utility to graph the polar equation over the given interval. Use the integration…

A: Given r = 2 sin(2 cos θ), [0, π]

Q: The origin in the rectangular coordinate system coincides with the_______ in polar coordinates.The…

A: Given: The origin in the rectangular coordinate system coincides with the_______ in polar…

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Consider the following polar equation: r=2sinθ Differentiate r with respect to θ:…

Q: Prove that both polar curves are symmetric with respect to the polar axis. Find the polar…

A: For symmetry with respect to the polar axis ( x-axis). We replace (r,Ѳ) by (r,-Ѳ) to determine…

Q: roblem 1: onvert from rectangular to polar form: a) 2 + 2v3i b) 3- 4i =) V3 - i

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Convert to a polar coordinates. 11. (-4,4) lar form. Show work on separate paper.

A:

Q: Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates.…

A:

Q: 7. Translate the polar equation into rectangular coordinates and graph it. Set up and evaluate the…

A: Use polar equation into simple equation

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: