2016年10月21日 · A = 1/2 ∫80 cos 2 θ - 8cosθ -16 dθ A = ∫ 40 cos 2 θ - ∫4cosθ - ∫8 dθ 0 to 30 I hope that you can do the rest because i"m tired of typing math.

2020年12月2日 · 1/2 · ∫ [ -7 + 14 cos(θ) ] dθ; evaluated from - π/3 to π / 3 The limits of integration are∫ from - π / 3 to π / 3, and the graph is symmetrical; therefore, one may obtain the same result by integrating from 0 to π /3 and multiplying the above integral by 2 obtaining:

2020年3月31日 · cos θ = 1/2 so θ = ± π/3. In polar coordinates, area is ∫1/2 r 2. so here we want the larger area: 1/2 ∫(9cosθ) 2 dθ. and the smaller area: 1/2 ∫(4+cosθ) 2 dθ (both are from -π/3 to π/3) Then the area is the big area minus the small area. If we're solving these integrals without a calculator we will need the trig identity cos 2 ...

Q: Obtain the parametric equations of: An epicycloid curve described by a point on the circumference of… A: Q: The intercepts on the horizontal axis are (pi/6 ,0) and (5pi/6, 0). graph the corresponding polar…

Paula G. asked • 10/01/15 Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin 8x = x cos 2y, (p/2, p/4)

Mia L. asked • 10/15/15 Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

2022年6月24日 · One way to do this is to draw the curves and see that the areal region can be described as the differences in the "wedge-shapes" of r 1 and the portion of the wedge shape in r 2 for the range of theta that is of interest.

Consider the following curve. x = sin(6t), y = -cos(6t), z = 24t Using the given parametric equations, give the corresponding vector equation r(t). r(t) = (sin (6t), - cos (6t),241) Find r'(t) and Ir'(t)\. r'(t) = |r'(t) = √612 (6 cos (61),6 sin (6t),24) Find the equation of the normal plane of the given curve at the point (0, 1, 4x). -6x+12z-48=0 x Now consider the osculating plane of the ...

2021年3月4日 · Find the area of the region that is inside the curve r = sin θ and outside the curve r = 1 + cos θ.  Your work must include the integral, but you may use your calculator to find the area to 3 decimal places.

2021年4月4日 · The figure above shows the graph of the polar curve r=1−2cosθ for 0≤θ≤π and the unit circle r=1.  (a) Find the area of the shaded region in the figure. Question 2 (b) Find the slope of the line tangent to the polar curve r=1−2cosθ at the point where x=−2. Show the computations that lead to your answer. Question 3