What is the integral from-pi/4 to pi/4 of sec(x) ?

The integral from-pi/4 to pi/4 of sec(x) is ln(1+sqrt(2))-ln(-1+sqrt(2))

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integral from-pi/4 to pi/4 of sec(x)

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

ln (1 + 2) - ln (- 1 + 2)

Decimal

1.76274 \dots

Solution steps

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

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= [ln ∣ tan (x) + sec (x) ∣]_{- \frac{π}{4}}^{\frac{π}{4}}

Compute the boundaries:

ln (1 + 2) - ln (- 1 + 2)

= ln (1 + 2) - ln (- 1 + 2)

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What is the integral from-pi/4 to pi/4 of sec(x) ?
The integral from-pi/4 to pi/4 of sec(x) is ln(1+sqrt(2))-ln(-1+sqrt(2))