All Tasks
Integral using variable change
Using the change of variables $u=e^x$, the integral
$$\int\frac{1}{e^x+1}dx$$ is:
# Integration calculus
Learning
13
Primitive concept
Without solving the integral tell if the equality is true (T) or false (F)
$\int \frac{\sin(x)}{cos^2(x)}dx=\sec(x)+C$
# Integration calculus
Reasoning
13
Primitive concept
Without solving the integral tell if the equality is true (T) or false (F)
$\int x\sin(x)dx=x \cos(x)-\sin(x)+C$
# Integration calculus
Training
13
Support for finding out of hypotenuse
Which one of the sides is the hypotenuse?
# Pythagorean theorem
Training
9
The top-right diagonal
Likewise, looking at this spiral of numbers, find the few first items along the diagonal, beginning with 4, 16, 36,...
# Sequences
# Natural numbers
Modeling
5
What is bigger?
Consider the unit squares in the infinite square lattice in the plane on one side, and the integer numbers, as well infinitely many of them, on the other side. What can you say about them?
# Set theory
Modeling
13