intégration par partie

bonsavoir.be
Quiz by bonsavoir.be, updated more than 1 year ago
bonsavoir.be
Created by bonsavoir.be almost 6 years ago
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Description

Maths Quiz on intégration par partie, created by bonsavoir.be on 07/15/2015.

Resource summary

Question 1

Question
\[\int x e^x dx = \]
Answer
  • \[x f(x) - \int f(x) dx \]
  • \[x f(x) + \int f(x) dx \]
  • \[x f(x) - \int f'(x) dx \]
  • aucune de ses solution

Question 2

Question
\[\int x ln(x) dx = \]
Answer
  • \[\int e^x g(x) dx - \int e^x g'(x) dx \]
  • \[e^x g(x) - \int e^x g'(x) dx \]
  • \[e^x g(x) + \int e^x g(x) dx \]
  • \[\int e^x g(x) dx + \int e^x g'(x) dx \]

Question 3

Question
\[\int x sin(x) dx = \]
Answer
  • \[sinx - cos(x) \]
  • \[sinx+ x cos(x) \]
  • \[cosx - x sin(x) \]
  • \[sinx - x cos(x) \]

Question 4

Question
\[\int \frac {x^2}{e^x} dx = \]
Answer
  • \[x (lnx + 1) \]
  • \[x (lnx - 1) \]
  • \[x lnx - 1 \] \]
  • \[\ (lnx -x) \] \]

Question 5

Question
\[\int \frac {ln(x)}{x^2} dx = \]
Answer
  • x^-²
  • \[\-frac {1 + ln(x)}{x} \]
  • \[ \frac{x^2 ln(x)}{2} - \frac{x²}{4}\]
  • ---

Question 6

Question
\[\int x^2 cos(x) dx = \]
Answer
  • \[\e^x (x-1) \]
  • -
  • --
  • ---

Question 7

Question
\[ \int sin x e^x dx = \]
Answer
  • 1
  • 2
  • 3
  • 4

Question 8

Question
\[ \int \frac {cos(x)}{e^x} dx = \]
Answer
  • redd
  • \[ bold \red 5 \]
  • 3
  • 4

Question 9

Question
\[ \int cos(x)^2 dx = \]
Answer
  • -
  • 2
  • ---
  • \[ \frac{1}{2} (x + sin(x) cos(x) = \]

Question 10

Question
\[ \int \frac {dx}{cos(x)} = \int \frac {1}{cos(x)} * \frac {sin(x)}{sin(x)} dx = \int \frac {sin(x)}{cos(x)} * \frac {1}{sin(x)} dx = \int tg(x) * \frac {1}{sin(x)} dx = \]
Answer
  • \[\frac {{\color{red} sin(x)}}{{\color{red} sin(x)}} }\]
  • --
  • ---
  • ----
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