What is the integral from pi/6 to pi/3 of tan(x)sec^2(x) ?

The integral from pi/6 to pi/3 of tan(x)sec^2(x) is 4/3

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integral from pi/6 to pi/3 of tan(x)sec^2(x)

\int_{\frac{π}{6}}^{\frac{π}{3}} tan (x) sec^{2} (x) d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{3}} tan (x) sec^{2} (x) d x

Apply u-substitution

: \int_{\frac{3}{3}}^{3} u d u

= \int_{\frac{3}{3}}^{3} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{\frac{3}{3}}^{3}

= [\frac{u ^{2}}{2}]_{\frac{3}{3}}^{3}

\frac{3}{3} = \frac{1}{3}

= [\frac{u ^{2}}{2}]_{\frac{1}{3}}^{3}

Compute the boundaries:

\frac{4}{3}

= \frac{4}{3}

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What is the integral from pi/6 to pi/3 of tan(x)sec^2(x) ?
The integral from pi/6 to pi/3 of tan(x)sec^2(x) is 4/3