| ucf26-004 Let C be the curve given in parametric equations for \( 0 < t \leq 1 \) by \( x(t) = t \cos (2\pi \ln t) , y(t) = t \sin (2\pi \ln t) \) .
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| ucf26-005 A bicycle moving with velocity \( v \) has a rear wheel of radius \( R \) with a reflector at a distance \( r \) from the center.
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| ucf27-001 These integrals are useful in trigonometric substitution. You should remember them or be able to evaluate them quickly.
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| ucf27-004 Evaluate the following integrals, where \( a, b, c \) are constants and \( a>0 \).
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| ucf27-005 Evaluate each of the following integrals using the substitution \( x=\sin\theta \) . In the last three problems, check by using another method.
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