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

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

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

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

33

Decimal Notation

5.19615 \dots

Solution steps

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

Apply u-substitution

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

= \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

y = x^{3}, (- 2, - 8)

n = 1 \sum \infty \frac{( - 3 ) ^{n}}{n}

\frac{d}{d x} (x - x^{- 1})

y^{^{'}} - \frac{3}{x} y = \frac{y ^{4}}{x ^{2}}

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