What is the integral from 0 to pi of xsec^2(x) ?

The integral from 0 to pi of xsec^2(x) is 0

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integral from 0 to pi of xsec^2(x)

\int_{0}^{π} x sec^{2} (x) d x

0

Solution steps

\int_{0}^{π} x sec^{2} (x) d x

Apply Integration By Parts

= [x tan (x) - \int tan (x) d x]_{0}^{π}

\int tan (x) d x = - ln ∣ cos (x) ∣

= [x tan (x) - (- ln ∣ cos (x) ∣)]_{0}^{π}

Simplify

= [x tan (x) + ln ∣ cos (x) ∣]_{0}^{π}

Compute the boundaries:

0

= 0

What is the integral from 0 to pi of xsec^2(x) ?
The integral from 0 to pi of xsec^2(x) is 0