Calculati

[Beniamin Bogosel]

Calculati:
a) \( \int_0^1\left(\int_y^1 e^{x^2} dx\right)dy \)
b) \( \int_0^1\left(\int_y^1 \cos{x^2} dx\right)dy \)
c) \( \int_0^1\left(\int_y^1 G(x^2) dx\right)dy \) unde \( G \in \int g \).

[Marius Mainea]

a) Integrind prin parti \( \int_0^1\left(\int_y^1 e^{x^2} dx\right)dy=y\int_y^1e^{x^2}dx\mid_0^1-\int_0^1y\cdot(-e^{y^2})dy=\frac{e^{y^2}}{2}|_0^1=\frac{e-1}{2} \)
b) Analog.
c) Analog.