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

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

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

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

4

Solution steps

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

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

\frac{\partial}{\partial x} (x^{2} + 8 x y + 3 y^{2})

\frac{x ^{2}}{x - 5}

n \to \infty lim (n + 1)

\int \frac{x ^{2}}{x ^{2} + 3} d x

\frac{\partial}{\partial x} (4 x - y^{2} - 4)

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