he area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1- cos 0).

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

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A: We need to integrate∫sin52xcos2x dx

Q: 2. [e1/² cos 2tdt Set/2

A:

Q: Graph the cardioid r = a(1+ sin®), a< 0?

A: We are given that r=a(1+sin∅), a&lt;0 Here as we know that sin∅ is always greater than equal to -1.…

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

A:

Q: 2t dt (use trigonometric substituion) V9 – 4t2 -

A:

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

A: Consider the given function r=1+sinθ

Q: (b) Find the entire length of the cardioid r = a(1+cos0).

A:

Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

A:

Q: Ssin8 (3z) cos5 (3z) dz

A:

Q: The integration of cosx is

A: Recall: Definition of Integration:      In mathematics , Integration is a technique to finding a…

Q: State the amplitude of the sinusoid A=-2/7 B=-5/7 x=b² sin(a²t - b)

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Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

A:

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Find : y``+ 2y` + y = cos²x turn to 1-cos2x/2

A:

Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: Find dr de = dr de (5+ sec 0) sin 0

A: