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

The integral from 0 to pi/3 of sec^4(x) is 2sqrt(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^4(x)

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

23

Decimal

3.46410 \dots

Solution steps

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

Rewrite using trig identities

= \int_{0}^{\frac{π}{3}} (1 + tan^{2} (x)) sec^{2} (x) d x

Apply u-substitution

: \int_{0}^{3} 1 + u^{2} d u

= \int_{0}^{3} 1 + u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{3} 1 d u + \int_{0}^{3} u^{2} d u

\int_{0}^{3} 1 d u = 3

\int_{0}^{3} u^{2} d u = 3

= 3 + 3

Simplify

= 23

f (x) = 8 - x^{2}

\int u^{1} d u

y^{(\frac{1}{2})} \frac{d y}{d x} + y^{(\frac{3}{2})} = 1, y (0) = 9

f (x) = cos (x) - 1

\frac{d}{d x} (e^{2 x})

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