What is the integral from 0 to pi/3 of 4sec^3(x) ?

The integral from 0 to pi/3 of 4sec^3(x) is 4(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 4sec^3(x)

\int_{0}^{\frac{π}{3}} 4 sec^{3} (x) d x

4 (3 + \frac{1}{2} ln (2 + 3))

Decimal Notation

9.56211 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 4 sec^{3} (x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{3}} sec^{3} (x) d x

Apply Integral Reduction

= 4 ([\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)

= 4 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3))

Simplify

4 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3)) : 4 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3))

= 4 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{3}} + \frac{1}{2} ln (2 + 3))

Compute the boundaries:

3

= 4 (3 + \frac{1}{2} ln (2 + 3))

\int \frac{2}{3} y e^{y} d y

\frac{d}{d x} (- 2 x^{3} - 7 x + 5)

\frac{\partial}{\partial x} (y^{0.25} x^{0.75})

f (x) = x^{π}

\frac{d x}{d y} = x

What is the integral from 0 to pi/3 of 4sec^3(x) ?
The integral from 0 to pi/3 of 4sec^3(x) is 4(sqrt(3)+1/2 ln(2+sqrt(3)))