What is the integral from-pi/4 to pi/4 of csc^2(x) ?

The integral from-pi/4 to pi/4 of csc^2(x) is diverges

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integral from-pi/4 to pi/4 of csc^2(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} csc^{2} (x) d x

diverges

Solution steps

\int_{- \frac{π}{4}}^{\frac{π}{4}} csc^{2} (x) d x

Take the denominator(s) of

csc^{2} (x)

and compare to zero:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- \frac{π}{4}}^{0} csc^{2} (x) d x + \int_{0}^{\frac{π}{4}} csc^{2} (x) d x

\int_{- \frac{π}{4}}^{0} csc^{2} (x) d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{3} x^{2} - 2 x - 4 d x

\int_{0}^{4} (3 x^{2} + 4 x + 7) d x

\int_{5}^{8} x^{2} d x

\int_{0}^{6} \frac{x}{9 + 2 x ^{2}} d x

\int_{0}^{3} \frac{x}{1 + 6 x ^{2}} d x

What is the integral from-pi/4 to pi/4 of csc^2(x) ?
The integral from-pi/4 to pi/4 of csc^2(x) is diverges