Download MATH 1920-01 SPRING CALCULUS II 2006 MIT Integration Bee

MATH 1920-01
SPRING
CALCULUS II
2006
MIT Integration Bee
The MIT Integration Bee is a yearly competition open to undergraduates. The initial
phase of the competition consists of an hour-long written competition consisting of forty
integration problems. The subsequent phases are handled like a Spelling Bee. At the
end of the 1991 competition, there were four finalists, who were given the following four
problems.
Z
cot x
ex (x − 2)
dx
dx
3
x
log(sin x)
Z
Z
2
x sec x dx
x sec x(x tan x + 2) dx.
Z
The problems for the first round are given below. Have fun!
Z
1.
e1991x dx
Z
2.
log x dx
Z
(sin x − cos x)2 dx
3.
Z
2
Z
5.
Z
x +x
Z
7.
Z
8.
Z
x
dx
dx
πx
ee
6.
9.
2
esin x ecos
4.
x4
dx
x
dx
+1
dx
x log x
e5x + e7x
dx
ex + e−x
1
Z
xex sin x dx
10.
Z
√
3
11.
x+1
dx
x2 + 2x + 2
Z
12.
(cosh x − sinh x) dx
Z
13.
x2 + 1
dx
x4 − x 2 + 1
Z
sec3 x dx
14.
Z
15.
16.
dx
sec x + tan x sin x
Z p
Z
17.
−1 + 2/(1 + 3x) dx
sin x esec x
dx
cos2 x
Z
18.
πx2
Z
19.
Z
20.
+ tan
−1
dx
x + x2 tan−1 x + π
dx
12 + 13 cos x
x3 + 1
dx
x+1
Z
e1991 dx
21.
Z
22.
x2
dx
− 10x + 26
x2
dx
− 11x − 26
Z
23.
Z
24.
(1 − 4x4 )−1/2
dx
(4x)−1
Z
25.
(log x + 1)xx dx
2
Z
26.
(cos 2x)(sin 6x) dx
Z
√
27.
dx
√ dx
x(1 + x)
Z
e1/x x−3 dx
28.
Z
29.
Z
30.
√
csc x − sin x dx
x2 + 1
dx
x3 + 1
Z
42x dx
31.
Z
x5 ex dx
32.
Z
2
xex dx
33.
Z
34.
(x2
Z
35.
ex
dx
+ 1)2
dx
+ e−x
Z
36.
tan x log | sec x| dx
Z
37.
cos(sin x) cos x dx
Z
38.
dx
−9
x2
Z
39.
40.
√
Z √
π dx
16 − e2
tan x dx
3