What is the integral from 0 to pi/2 of sec^3(x) ?

The integral from 0 to pi/2 of sec^3(x) is diverges

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integral from 0 to pi/2 of sec^3(x)

\int_{0}^{\frac{π}{2}} sec^{3} (x) d x

diverges

Solution steps

\int_{0}^{\frac{π}{2}} sec^{3} (x) d x

Apply Integral Reduction

= [\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{2}} + \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} sec (x) d x

\int_{0}^{\frac{π}{2}} sec (x) d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{2} x^{2} + x^{- 2} d x

\int_{- 7}^{0} \frac{2}{x ^{\frac{2}{3}}} d x

\int_{0}^{π} (9 e^{x} + 9 sin (x)) d x

\int_{\frac{π}{2}}^{π} x^{2} sin (\frac{x}{2}) d x

\int_{0}^{4} (5 + 7 x) d x

What is the integral from 0 to pi/2 of sec^3(x) ?
The integral from 0 to pi/2 of sec^3(x) is diverges