استخرج قيمة التكامل غير المحدود: \( \int_{-1}^{0} e^{-x^2} \, dx \)

Calculate the integral of \( f(x, y)=\left(x^{2}+y^{2}\right)^{-2} \) over the region \( x^{2}+y^{2} \leq 25, x \geq \frac{5}{\sqrt{2}} \) by changing to polar coordinates. (Use symbolic notation and fractions where needed.) \( \iint_{D} f(r, \theta) d r d \theta=\square \) help (fractions).

INSTRUCCIONES: Resuelvi 1. \( \int_{1}^{4} x^{2} d x= \)

25. \( N=\frac{p+q}{p+r}, \quad p=u+v w, \quad q=v+u w, \quad r=w+u v \) \( \frac{\partial N}{\partial u}, \frac{\partial N}{\partial v}, \frac{\partial N}{\partial w} \quad \) donde \( u=2, v=3, w=4 \)

3. El ingreso mensual por concepto de la venta de \( x \) unidades está dado por: \[ \mathrm{R}(x)=12 x-0,01 x^{2} \text { dolares } \]

Tarea \( \int 5 d x= \) \( \int \frac{d x}{3}= \) \( \int x d x= \) \( \int 3 d u= \)