Call an improper definite integral type 1 if it is improper because the interval of integration is infinite.

Call it type 2 if it is improper because the function takes on an infinite value within the interval of integration.

Classify the type(s) for each of the following improper integrals.

? Type 1 Type 2 Type 1 and Type 2  1. $\displaystyle \int_{-\infty}^{\,0} {\frac{1}{x^2+5}}\, dx$

? Type 1 Type 2 Type 1 and Type 2  2. $\displaystyle \int_{0}^{\,2} {\frac{x}{x^2-5x+6}}\, dx$

? Type 1 Type 2 Type 1 and Type 2  3. $\displaystyle \int_{0}^{\,\pi/2} {\sec(x)}\, dx$

? Type 1 Type 2 Type 1 and Type 2  4. $\displaystyle \int_{1}^{\,\infty} {x^4e^{-x^4}}\, dx$