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1124worksheet3

# 1124worksheet3 - (5 Use the Fundamental Theorem of Calculus...

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Polytechnic Institute of NYU MA 1124 Worksheet 3 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 15 2 15 3 15 4 15 5 15 6 15 7 10 Total 100

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Your signature: (1) Find the general antiderivative. (a) f ( x ) = sin x + 3 cos x (b) g ( t ) = e t + t 2 (c) r ( z ) = z 5 + z 2 + z
Your signature: (2) Find the indefinite integrals. (a) Z (1 + x ) 2 x dx (b) Z 1 3 z dz (c) Z πe y dy

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Your signature: (3) Find the area between the graph of f and the x -axis. (a) f ( x ) = (2 x 2 + 1) 2 , x [0 , 1] (b) f ( x ) = x 2 - 4, x [1 , 2] (c) f ( x ) = x + 1, x [3 , 8]
Your signature: (4) Find the area of the region bounded by the curves. (a) y = 5 - x 2 , y = 3 - x (b) y = x , y = sin x , x = π/ 2 (c) y = x 2 , y = - x , x

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Unformatted text preview: (5) Use the Fundamental Theorem of Calculus to ﬁnd the derivative of the given func-tion. (a) g ( x ) = Z x 3 ( t 2-1) 20 dt (b) h ( x ) = Z √ x cos x s 2 s 2 + 1 ds (c) y ( x ) = Z π 4 x +1 x 2 t sin( t 4 ) dt Your signature: (6) Find the derivative of each function. (a) g ( x ) = Z 3 x 2 x u-1 u + 1 du (b) g ( x ) = Z x 2 tan x 1 √ 2 + t 4 dt (c) y = Z x 3 √ x √ t sin tdt Your signature: (7) Find H (2) given that H ( x ) = Z x 3-4 2 x x 1 + √ t dt...
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1124worksheet3 - (5 Use the Fundamental Theorem of Calculus...

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