What is the integral from 0 to pi/4 of csc(x) ?

The integral from 0 to pi/4 of csc(x) is diverges

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integral from 0 to pi/4 of csc(x)

\int_{0}^{\frac{π}{4}} csc (x) d x

diverges

Solution steps

\int_{0}^{\frac{π}{4}} csc (x) d x

Apply u-substitution

: \int_{0}^{2 - 1} \frac{1}{u} d u

= \int_{0}^{2 - 1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{0}^{2 - 1}

Compute the boundaries:

diverges

= diverges

\int_{0}^{1} \frac{arctan ( x )}{x} d x

\int_{- 1}^{1} arccos (x) d x

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

\int_{0}^{4} \frac{x}{16 - x ^{2}} d x

\int_{5}^{11} \frac{1}{x ^{2}} d x

What is the integral from 0 to pi/4 of csc(x) ?
The integral from 0 to pi/4 of csc(x) is diverges