All Tasks

Area T-B

The area of the figure can be calculated by:
 
# Application

Training
13

Area T-I

The area of the figure can be calculated by:
 
# Application

Training
13

Definite Integral - IS (A)

Consider the integral $\displaystyle I=\int_{0}^{a} 2\sqrt{a^2-x^2}dx$ and the change of variable $x=a \sin(t)$. So $I$ comes equal to:
 
# Definite integral

Reasoning
13

Definite Integral - IS (I)

Consider the integral $\displaystyle I=\int_{\frac{\pi}{4}}^{\frac{\pi}{3}} f(x)dx$ and the change of variable $x= \arctan(t)$. So $I$ comes equal to:
 
# Definite integral

Reasoning
13

Definite Integral - MIP (I)

The value of the integral $\int_1^{e}\ln(x)dx$ is:
 
# Definite integral

Training
13

Definite Integral (I)

The value of the integral $\displaystyle \int_0^1 \frac{y}{y^2+1}dy$ is:
 
# Definite integral

Training
13