Final Exam questions 2012 PDF

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Final Exam questions for the year 2012...

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2012 Integration Bee

Qualifying Test January 13, 2012

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This is the qualifying test for the 2012 Integration Bee, held on Friday, January 13th at 4PM–6PM in room 4-149. Finalists will be notified by email by midnight tonight (12:00am, Saturday, January 14th). You have 20 minutes to solve these 25 integrals. Each integral is worth 1 point. In order to receive full credit you must express your answer in terms of x for indefinite integrals or simplified expressions in terms of constants for definite integrals, and your answer must be circled. There is no partial credit. The “log” symbol denotes the natural logarithm. In your answers, it is not necessary to include the arbitrary constant C nor the absolute value sign around the argument of a logarithm. Note: The problems are not arranged in order of difficulty. Budget your time carefully!

Good Luck!

Z

1.

√

dx x−1

2.

Z

x1/4 log(x) dx

3.

Z

dx √ √ (1 + x) x − x2

4.

Z

5.

Z

6.

Z

√

dx √ x( 4 x + 1)10

1

sin(cos−1 (x)) dx 0

√

dx 1 − 4x − x2

7.

8.

9.

Z

1/2

1/4

Z

Z



π 2

0

  1 dx log x

dx 1 + sin(x)

√

2011 1

√

x √ dx 2012 − x + x

x−1 √ dx (x + 1) x3 + x2 + x

10.

Z

11.

Z

12.

 Z  sin(x) cos(x) log(x) + dx x

0

x4 + 4x3 + 6x2 + 4x + 1 dx x3 − 3x2 + 3x − 1 −1

Z

13.

14.

15.

Z

Z

1/2 0

dx x3 − x

x sin−1 (x) √ dx 1 − x2

1 0

x(1 − x)99 dx

16.

17.

18.

Z

π/2 0

sin(4x) dx sin(x)

1

Z

1 + x3

Z

√

x− 2 1

dx

dx 2x2 − 1

19.

Z

√

20.

Z

x dx x4 + 4

21.

Z

dx ex − 1

2 dx (cos(x) − sin(x))2

22.

23.

24.

x cosh(x) dx sinh(x)2

Z

Z

2

√ x5 1 + x3 dx

0

Z

0

1

x7 − 1 dx log(x)

25.

Z p

csc(x) − sin(x) dx...