What is the integral from 0 to pi of sec^2(t/4) ?

The integral from 0 to pi of sec^2(t/4) is 4

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integral from 0 to pi of sec^2(t/4)

\int_{0}^{π} sec^{2} (\frac{t}{4}) d t

4

Solution steps

\int_{0}^{π} sec^{2} (\frac{t}{4}) d t

Apply u-substitution

: \int_{0}^{\frac{π}{4}} sec^{2} (u) \cdot 4 d u

= \int_{0}^{\frac{π}{4}} sec^{2} (u) \cdot 4 d u

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{4}} sec^{2} (u) d u

Use the common integral:

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

= 4 [tan (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

1

= 4 \cdot 1

Simplify

= 4

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What is the integral from 0 to pi of sec^2(t/4) ?
The integral from 0 to pi of sec^2(t/4) is 4