What is the integral from 0 to pi/2 of 2cos^2(x) ?

The integral from 0 to pi/2 of 2cos^2(x) is pi/2

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/2 of 2cos^2(x)

\int_{0}^{\frac{π}{2}} 2 cos^{2} (x) d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 2 cos^{2} (x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{π}{2}} cos^{2} (x) d x

Rewrite using trig identities

= 2 \cdot \int_{0}^{\frac{π}{2}} \frac{1 + cos ( 2 x )}{2} d x

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} 1 + cos (2 x) d x

Apply the Sum Rule:

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

= 2 \cdot \frac{1}{2} (\int_{0}^{\frac{π}{2}} 1 d x + \int_{0}^{\frac{π}{2}} cos (2 x) d x)

\int_{0}^{\frac{π}{2}} 1 d x = \frac{π}{2}

\int_{0}^{\frac{π}{2}} cos (2 x) d x = 0

= 2 \cdot \frac{1}{2} (\frac{π}{2} + 0)

Simplify

2 \cdot \frac{1}{2} (\frac{π}{2} + 0) : \frac{π}{2}

= \frac{π}{2}

x \to - 0 lim (\frac{6 x}{x ^{4}})

\frac{- 4 e ^{(- s)} \cdot ( e ^{3} )}{( ( s - 3 ) ( s - 4 ) ( s + 1 ) )}

y^{^{'}} + y = e^{- 2 t}

\int_{6}^{8} \frac{20}{( x - 6 ) ^{3}} d x

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

What is the integral from 0 to pi/2 of 2cos^2(x) ?
The integral from 0 to pi/2 of 2cos^2(x) is pi/2