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IntegrationQuestion and Answers: Page 19

Question Number 200930 Answers: 0 Comments: 1

If I_n =∫_0 ^1 (1−x^4 )^n dx and (I_n /I_(n−1) )=((λn)/(λn+1)) then find λ

$I f I_{n} = \int_{0}^{1} {(1 - x^{4})}^{n} d x a n d \frac{I_{n}}{I_{n - 1}} = \frac{λ n}{λ n + 1}$ $t h e n f i n d λ$

Question Number 200844 Answers: 2 Comments: 2

Question Number 200802 Answers: 1 Comments: 0

Question Number 200801 Answers: 1 Comments: 0

Question Number 200748 Answers: 2 Comments: 0

Question Number 200747 Answers: 2 Comments: 0

Question Number 200737 Answers: 0 Comments: 0

Solve: The position vector of a particle at any time t is given by r_− =(acoswt)i+(asinwt)j+bt^2 k (a) show that,although the speed of the particle increases with time,the magnitude of the acceleration is always constant (b) describe the motion of the particle geometrically

$S o l v e : T h e p o s i t i o n v e c t o r o f a p a r t i c l e a t a n y t i m e t$ $i s g i v e n b y \underline{r} = (a c o s w t) i + (a s i n w t) j + {b t}^{2} k$ $(a) s h o w t h a t, a l t h o u g h t h e s p e e d o f t h e p a r t i c l e$ $i n c r e a s e s w i t h t i m e, t h e m a g n i t u d e$ $o f t h e a c c e l e r a t i o n i s a l w a y s c o n s t a n t$ $(b) d e s c r i b e t h e m o t i o n o f t h e p a r t i c l e g e o m e t r i c a l l y$

Question Number 200736 Answers: 0 Comments: 0

Solve: A particle moves along the space curve r_− =(t^2 +t)i+(3t−2)j+(2t^3 −4t^2 )k. find (a)velocity (b)speed or magnitude of velocity (c)acceleration (d)magnitude of acceleration at time t=2

$S o l v e : A p a r t i c l e m o v e s a l o n g t h e s p a c e$ $c u r v e \underline{r} = (t^{2} + t) i + (3 t - 2) j + (2 t^{3} - 4 t^{2}) k .$ $f i n d$ $(a) v e l o c i t y$ $(b) s p e e d o r m a g n i t u d e o f v e l o c i t y$ $(c) a c c e l e r a t i o n$ $(d) m a g n i t u d e o f a c c e l e r a t i o n a t t i m e t = 2$