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1124worksheet5

# 1124worksheet5 - (a Z cos 4 t cos 5 tdt(b Z 1 cos 3 x dx...

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Polytechnic Institute of NYU MA 1124/1424 Worksheet 5 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 15 5 10 6 10 7 10 8 10 9 15 Total 100 1

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2 (1) Evaluate the integrals by parts. (a) Z x 3 e x 2 dx (b) Z (3 x + 4) e 2 x dx
3 (2) Evaluate the integrals by parts. (a) Z ln xdx (b) Z sin(ln x ) dx

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4 (3) Evaluate the integrals by parts. (a) Z cos x · ln (sin x ) dx (b) Z x · arcsin( x 2 ) dx
5 (4) Evaluate the integrals. (a) Z 1 0 ln(1 + x 2 ) dx (b) Z 1 / 4 0 arcsin 2 xdx

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6 (5) Use integration by parts to show that: (a) Z (ln x ) n dx = x (ln x ) n - n Z (ln x ) n - 1 dx (b) Z e ax sin bxdx = e ax ( a sin bx - b cos bx ) a 2 + b 2 + C
7 (6) Use the table of integrals to evaluate the integrals. You may need to transform the

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Unformatted text preview: (a) Z cos 4 t cos 5 tdt (b) Z 1 cos 3 x dx 8 (7) Use the table of integrals to evaluate the integrals. You may need to transform the integrand ﬁrst. (a) Z 1 x 2 + 6 x + 9 dx (b) Z 1 50-2 y 2 dy 9 (8) Use the table of integrals to evaluate the integrals. You may need to transform the integrand ﬁrst. (a) Z x 3 cos x 2 dx (b) Z x sin 3 x 2 dx 10 (9) Use the table of integrals to evaluate the integrals. You may need to transform the integrand ﬁrst. (a) Z dx √ 16 x 2 + 36 (b) Z dx √ 81-25 x 2...
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