#### 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
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#### 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
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#### 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

#### Definite Integral (B)

If $f$ is a real function of a real variable, is continues and $F'(x)=f(x), \forall x \in \mathbb{R}$, so $\int_1^3 f(2x)dx$ is:

# Definite integral

Training
13

#### Modelling linear functions

Imagine that you want to buy some pens. In the shop near home one pen cost 0,80 euro, online one pen cost 0,60 euro but the shipping fees are 3 euro. How many pens you have to buy in order to spend the same money in each shop?

# Linear functions

Training
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