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

The integral from 0 to pi/4 of 2sec(t) is 2ln(1+sqrt(2))

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

\int_{0}^{\frac{π}{4}} 2 sec (t) d t

2 ln (1 + 2)

Decimal

1.76274 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 2 sec (t) d t

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 (t) d t

Use the common integral:

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

= 2 [ln ∣ tan (t) + sec (t) ∣]_{0}^{\frac{π}{4}}

Compute the boundaries:

ln (1 + 2)

= 2 ln (1 + 2)

What is the integral from 0 to pi/4 of 2sec(t) ?
The integral from 0 to pi/4 of 2sec(t) is 2ln(1+sqrt(2))