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1124worksheet6

# 1124worksheet6 - (b RIGHT(4 8(7 Estimate Z 12 x 2 dx...

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

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2 (1) Evaluate the given integral through the method of partial fractions. (a) Z 1 ( x - 4)( x - 5) dx (b) Z x x 2 - 3 x + 2 dx
3 (2) Evaluate the given integral through the method of partial fractions. (a) Z x 2 ( x - 1) 2 ( x + 1) 2 dx (b) Z 2 x 2 + 3 x 2 ( x - 1) dx

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4 (3) Evaluate the given integral through the method of partial fractions. (a) Z 1 x 3 - 1 dx (b) Z x 2 - 2 x - 1 ( x - 1) 2 ( x 2 + 1) dx
5 (4) Evaluate the integral. (a) Z 1 0 x - 1 x 2 + 2 x + 2 dx (b) Z 1 0 x x 2 + 4 x + 4 dx

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6 (5) Evaluate the integral. (a) Z e t e 2 t + 5 e t + 6 dt (b) Z sec 2 θ tan 3 θ - tan 2 θ
7 (6) Estimate Z 2 0 dx 4 + x 3 using:

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Unformatted text preview: (b) RIGHT(4) 8 (7) Estimate Z 12 x 2 dx using: (a) LEFT(12) (b) MID(6) 9 (8) Estimate Z 1 sin 2 πxdx using: (a) TRAP(4) (b) MID(3) 10 (9) Let f ( x ) be a decreasing and concave down on the interval [ a,b ]. Order the following approximations to the integral Z b a f ( x ) dx from smallest to largest. LEFT(n), RIGHT(n), MID(n), TRAP(n), Exact value. 11 (10) Show that the function g ( x ) = Ax 2 + Bx + C satisﬁes the condition Z b a g ( x ) dx = b-a 6 ± g ( a ) + 4 g ² a + b 2 ³ + g ( b ) ´ for every interval [ a,b ]....
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