ausecourpls.py

Created on February 23, 2024
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Primitives/Intégrales 2023/2024 Guillaume CHIVOT

Exercice 1 :
Calculer les intégrales suivantes :
1. R 0 à 1 dx / (x+1)^2
2. R 2 à 3 dt / (1−t)^3
3. R -3 à -2 du / (2u+1)
4. R 0 à 1 √(1 + 3x) dx
5. R 2 à 4 1 / (x ln(x)) dx
6. R 0 à 2 x / (3+x^2) dx
7. R 0 à 2 √(√(2)/3 √z) dz / (z^2+1)
8. R 1 à 2 ln(t) / t dt
9. R 0 à 1 (z+1) / (z^2+1) dz
10. R 0 à √3 2 / (t+3) / (t^2+4) dt
11. R 0 à 2 te^−t / 2 dt
12. R 2 à 7 √(u) / (u+2) du
13. R -1 à 0 x / (2+x^2)^2 dx
14. R 0 à ln(2) e^z / (1+e^z) dz
15. R 0 à π/4 tan(θ) dθ

Solution :
1. R 0 à 1 dx / (x+1)^2 = 1/2
2. R 2 à 3 dt / (1−t)^3 = -3/8
3. R -3 à -2 du / (2u+1) = ln(5)/3
4. R 0 à 1 (1 + 3x)^(1/2) dx = 14/9
5. R 2 à 4 1 / (x ln(x)) dx = ln(2)
6. R 0 à 2 x / (3+x^2) dx = ln(7)/3
7. R 0 à 2 √(√(2)/3 √z) dz / (z^2+1) = 1
8. R 1 à 2 ln(t) / t dt = (ln(2))^2 / 2
9. R 0 à 1 (z+1) / (z^2+1) dz = ln(2) + π/4
10. R 0 à √3 2 / (t+3) / (t^2+4) dt = ln(2) + π/2
11. R 0 à 2 te^−t / 2 dt = 1/2(1−e^−4)
12. R 2 à 7 √(u) / (u+2) du = 2
13. R -1 à 0 x / (2+x^2)^2 dx = -1/12
14. R 0 à ln(2) e^z / (1+e^z) dz = ln(3)/2
15. R 0 à π/4 tan(θ) dθ = 1/2 ln(2)

Exercice 2 :
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Exercice 3 :
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Exercice 4 :
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Exercice 5 :
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Exercice 6 :
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