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

The integral from 0 to pi/3 of sec^3(x) is sqrt(3)+1/2 ln(2+sqrt(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

3 + \frac{1}{2} ln (2 + 3)

Decimal Notation

2.39052 \dots

Solution steps

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

Apply Integral Reduction

= [\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} \cdot \int_{0}^{\frac{π}{3}} sec (x) d x

\int_{0}^{\frac{π}{3}} sec (x) d x = ln (2 + 3)

= [\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3)

Simplify

[\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3) : [\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3)

= [\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3)

Compute the boundaries:

3

= 3 + \frac{1}{2} ln (2 + 3)

\int \frac{x + 1}{4 - x ^{2}} d x

\frac{d}{d x} (5 x (sin (x) + cos (x)))

7 x^{2} y + y^{^{'}} = 6 x^{2}

y^{^{'''}} - 5 y^{^{''}} - 6 y^{^{'}} = 0

\frac{d}{d t} (t)

What is the integral from 0 to pi/3 of sec^3(x) ?
The integral from 0 to pi/3 of sec^3(x) is sqrt(3)+1/2 ln(2+sqrt(3))