What is the integral from 0 to pi of sec^2(t/6) ?

The integral from 0 to pi of sec^2(t/6) is 2sqrt(3)

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integral from 0 to pi of sec^2(t/6)

\int_{0}^{π} sec^{2} (\frac{t}{6}) d t

23

Decimal

3.46410 \dots

Solution steps

\int_{0}^{π} sec^{2} (\frac{t}{6}) d t

Apply u-substitution

: \int_{0}^{\frac{π}{6}} sec^{2} (u) \cdot 6 d u

= \int_{0}^{\frac{π}{6}} sec^{2} (u) \cdot 6 d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{0}^{\frac{π}{6}} sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= 6 [tan (u)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{3}

= 6 \cdot \frac{1}{3}

Simplify

= 23

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What is the integral from 0 to pi of sec^2(t/6) ?
The integral from 0 to pi of sec^2(t/6) is 2sqrt(3)