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}

= [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

\int_{- \infty}^{0} \frac{1}{5 x ^{3}} d x

\int_{0}^{\infty} 3 sin^{2} (a) d a

\int_{0}^{2} e^{x} cos (x) d x

\int_{0}^{π} x sin (x) cos (n x) d x

\int_{2}^{5} (\frac{5 x + 2}{3}) d x

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