(1) Find the area of the hypocycloid F (t) = (cos³ (t), sin® (t)), te [0, 27].

Q: dy sin x + (cos x)y = 0, y(7/6) = –2 TT dx

A:

Q: Let r(t) = (sin t, 2 cos t), t = (a) Find r'(t). (b) Find T(t).

A:

Q: Find dy. y = tan H 4 X + cos(4x)

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Q: Find (t), given 7(t) = (– 5t* – 1, 4 sin(2t), 4e*). = (?),

A: Given,

Q: A. J x² sin x dx B. f(x²+1) Inx dx C. fex cos x dx

A: For the integral ∫ x² sin(x) dx, we can use the method of integration by parts. The formula for…