Integration Pi
Vin Pioneers
November 29, 2023
Qualifier Round
Your Full Name:
Your Student ID:
Please write the result as simple as possible. +C is required for indefinite integrals. Only
the final result in your answer box counts, so you can write your draft work anywhere else.
No partial points are awarded.
Each problem has a weight depending on how difficult it is, varying from 1 to e points.
no. of contestants solved this problem
total no. of contestants
.
The weight is calculated by e
Tips: Problems are NOT ordered by difficulty.
Good luck, have fun!
Problem 1
Z
tan2 xdx
Problem 2
Z
e
e2
ln x
dx
x
Problem 3
Z
π
2
sin(2x)3 cos(x)dx
0
1
Integration Pi
Problem 4
Z
√
16 − 4x2 dx
2
0
Problem 5
Z
√
x
3
1 + x4
dx
Problem 6
Z
x2 sin(3x)dx
Problem 7
Z
1 + cot(x)
dx
1 − cot(x)
2
Vin Pioneers
November 29, 2023
Integration Pi
Problem 8
Z
sin 2x
dx
(2 cos x − sin 2x)(1 + sin x)
Problem 9
Z
x3
1
dx
+x
Problem 10
Z
dx
1 − e−x
Problem 11
Z
√
3
729
64
√
x
√ dx
x− 3x
3
Vin Pioneers
November 29, 2023
Integration Pi
Problem 12
2
Z
… q
» √
x x x x . . .dx
0
Problem 13
∞
Z
1
ln x
dx
x2
Problem 14
Z
cos(x) cos(2x) cos(4x)dx
Problem 15
Z
0
1
x
dx
1 + x4
4
Vin Pioneers
November 29, 2023