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

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

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

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

2

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= 2 [tan (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

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