2.2 Übungen
Aus Online Mathematik Brückenkurs 2
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Exercise 2.2:1
Calculate the integrals
| a) | \displaystyle \displaystyle \int_{1}^{2} \displaystyle\frac{dx}{(3x-1)^4}\quad by using the substitution \displaystyle u=3x-1, |
| b) | \displaystyle \displaystyle \int (x^2+3)^5x \, dx\quad by using the substitution \displaystyle u=x^2+3, |
| c) | \displaystyle \displaystyle \int x^2 e^{x^3} \, dx\quad by using the substitution \displaystyle u=x^3. |
Laden...Exercise 2.2:2
Calculate the integrals
| a) | \displaystyle \displaystyle\int_{0}^{\pi} \cos 5x\, dx | b) | \displaystyle \displaystyle\int_{0}^{1/2} e^{2x+3}\, dx |
| c) | \displaystyle \displaystyle\int_{0}^{5} \sqrt{3x + 1} \, dx | d) | \displaystyle \displaystyle\int_{0}^{1} \sqrt[\scriptstyle3]{1 - x}\, dx |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 2.2:3
Calculate the integrals
| a) | \displaystyle \displaystyle\int 2x \sin x^2\, dx | b) | \displaystyle \displaystyle\int \sin x \cos x\, dx |
| c) | \displaystyle \displaystyle\int \displaystyle\frac{\ln x}{x}\, dx | d) | \displaystyle \displaystyle\int \displaystyle\frac{x+1}{x^2+2x+2}\, dx |
| e) | \displaystyle \displaystyle\int \displaystyle\frac{3x}{x^2+1}\, dx | f) | \displaystyle \displaystyle\int \displaystyle\frac{\sin \sqrt{x}}{\sqrt{x}}\, dx |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 2.2:4
Use the formula
to calculate the integrals
| a) | \displaystyle \displaystyle\int \frac{dx}{x^2+4} | b) | \displaystyle \displaystyle\int \frac{dx}{(x-1)^2+3} |
| c) | \displaystyle \displaystyle\int \frac{dx}{x^2+4x+8} | d) | \displaystyle \displaystyle\int \frac{x^2}{x^2 +1}\, dx |
Answer
Solution a
Solution b
Solution c
Solution d
