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

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

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

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

33

Decimal

5.19615 \dots

Solution steps

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

Apply u-substitution

= \int_{0}^{\frac{π}{3}} sec^{2} (u) \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{3}} sec^{2} (u) d u

Use the common integral:

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

= 3 [tan (u)]_{0}^{\frac{π}{3}}

Compute the boundaries:

3

= 33

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