Qualifying round 2013 test PDF

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Qualifying round 2013 test...

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2013 MIT Integration Bee Qualifying Round

1

Z

2

Z 3

3

Z

4

Z 11

2

log( x ) − 2 log (2x ) dx e

−1

|x|

(log x )(cos x ) − (sin x )(1/x ) dx (log x )2 x3 − 3x2 + 3x − 1 dx

1

5

Z 2p

6

Z 6

0

0

7

Z

8

Z

9 10 11

12

dx

12 − 3x2 dx

x + (x − 3)7 + sin ( x − 3) dx

sin x

p

1 + tan2 x dx

x5 − x3 + x2 − 1 dx x4 − x3 + x − 1

Z 1 0

Z Z

0

14

Z 256

15

Z

e

16

Z

cos x cot x dx

17

Z

2 log x + (log x )2 dx

18

Z

x3 dx 1 + x2

19

Z

1 dx 2 − 2x + x2

20

Z

sin x log(sin x ) dx

21

Z

x dx 1 − x4

22

Z p

23

Z

24

Z π/4

1 dx 1 − sin x

25

Z

1

log x dx 1 dx 1 − e−x π

sin2 x cos2 x dx

√ Z 441 π sin(π x ) 0

13

Z

√

x

dx

tan2 x dx

0

( x − ⌊x ⌋)2 dx

√ 4

x

dx

12 − 3x2 dx

sec5 x tan3 x dx

−π/4

√

x x2 − 2

dx...