Integration

Answer all the questions below and press submit to see how many you got right.

id: 18925

Which of the following are true for a function $f$ and a real number $\lambda?$

  • $\int\limits_{0}^{9} f(x)+\lambda dx=\lambda\cdot 9+\int\limits_{0}^{9}f(x)dx$
    $\int\limits_{0}^{9}\lambda f(x)dx=\int\limits_{0}^{\lambda \cdot9}f(x)dx$
    $\int\limits_{0}^{9} f(x)+\lambda dx=\lambda+\int\limits_{0}^{9}f(x)dx$
    $\int\limits_{0}^{9}\lambda f(x)dx=\lambda\int\limits_{0}^{9}f(x)dx$
id: 18962

$\int\limits_{0}^{5} 5 dx=\lim_\limits{n\to\infty} \frac{5}{n}\sum\limits_{k=1}^{n}5=\lim_\limits{n\to\infty} \frac{5}{n}\cdot n\cdot 5=?$

id: 18965

$\int\limits_{0}^{2} 3 dx=\lim_\limits{n\to\infty} \frac{2}{n}\sum\limits_{k=1}^{n}3=\lim_\limits{n\to\infty} \frac{2}{n}\cdot n\cdot 3=?$