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1124worksheet4

# 1124worksheet4 - 6(5 Evaluate the indeﬁnite integral(a Z...

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Polytechnic Institute of NYU MA 1124/1424 Worksheet 4 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 12 2 12 3 10 4 10 5 10 6 10 7 12 8 12 9 12 Total 100 1

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2 (1) Find the general solution of the differential equation. (a) dy dx = x 4 + 5 x + 4 (b) dy dx = x π + π x (c) dF dt = t t + 1 t t (d) dr = 5 cos θ + 7 sin θ
3 (2) Find the solution of the initial value problem. (a) dP dt = 60 e t , P (1) = 180 e (b) dz dt = 6 t 2 + 4 t + 5, z (1) = 23 (c) dr dx = 5 + cos x , r ( π ) = 3

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4 (3) Find the solution of the initial value problem: d 2 s dt 2 = - 9 . 8, s (0) = 20, s 0 (0) = 10
5 (4) A car starts from rest at time t = 0 and accelerates at 12 meters/sec 2 . (a) How long does it take for the car to get up to 144 meters/sec? (b) How long does it take for the car to go 600 meters?

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Unformatted text preview: 6 (5) Evaluate the indeﬁnite integral. (a) Z x ( x 2-10) 2009 dx (b) Z x + 3 ( x 2 + 6 x ) 2 dx 7 (6) Evaluate the indeﬁnite integral. (a) Z dx (3 x + 1) 2 (b) Z x 4 √ x + 2 dx 8 (7) Evaluate the indeﬁnite integral. (a) Z t 2 cos(1-t 3 ) dt (b) Z cos 4 ( x ) sin ( x ) dx 9 (8) Evaluate the deﬁnite integral, if it exists. (a) Z 4 1 1 x 2 r 1 + 1 x dx (b) Z 1 ( x 4 + x ) 5 (4 x 3 + 1) dx 10 (9) (a) If f is continuous and Z 4 f ( x ) dx = 20, ﬁnd Z 2 f (2 x ) dx . (b) If f is continuous and Z 9 f ( x ) dx = 8, ﬁnd Z 3 xf ( x 2 ) dx ....
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