Question

Explain why each of the following integrals is improper.

Answer 1

\[\int\limits_{0}^{\pi/2}secx dx\]

Answer 2

because
\[\sec(\frac{\pi}{2})\] is undefined

Answer 3

\[\int\limits_{0}^{2} ((x)/(x^2 -5x +6)) dx\]

Answer 4

since
\[\sec(x)=\frac{1}{\cos(x)}\]and
\[\cos(\frac{\pi}{2})=0\]

Answer 5

second one because the denominator is zero at x = 2

Answer 6

\[\int\limits_{-infinite}^{0} ((1)/(x^2 +5)) dx\]

Answer 7

So the first one can be called a infinite discontinuity I'm guessing