What is the integral from 0 to pi/3 of 3sec(x) ?

The integral from 0 to pi/3 of 3sec(x) is 3ln(2+sqrt(3))

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integral from 0 to pi/3 of 3sec(x)

\int_{0}^{\frac{π}{3}} 3 sec (x) d x

3 ln (2 + 3)

Decimal Notation

3.95087 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 3 sec (x) d x

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{3}} sec (x) d x

Use the common integral:

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

= 3 [ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{3}}

Compute the boundaries:

ln (2 + 3)

= 3 ln (2 + 3)

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\int_{0}^{2 π} cos^{2} (t) sin (t) d t

What is the integral from 0 to pi/3 of 3sec(x) ?
The integral from 0 to pi/3 of 3sec(x) is 3ln(2+sqrt(3))