What is the integral from 0 to pi/2 of (5cos^2(x)) ?

The integral from 0 to pi/2 of (5cos^2(x)) is (5pi)/4

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 (5cos^2(x))

\int_{0}^{\frac{π}{2}} (5 cos^{2} (x)) d x

\frac{5 π}{4}

Decimal Notation

3.92699 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 5 cos^{2} (x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{\frac{π}{2}} cos^{2} (x) d x

Rewrite using trig identities

= 5 \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

= 5 \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

= 5 \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

= 5 \cdot \frac{1}{2} (\frac{π}{2} + 0)

Simplify

5 \cdot \frac{1}{2} (\frac{π}{2} + 0) : \frac{5 π}{4}

= \frac{5 π}{4}

\frac{\partial}{\partial y} (e^{x + y} sin (x - y))

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y (0) = 9, y (\frac{π}{4}) = 7

x (4.2)

\frac{d}{d x} (tan (x + c))

\int \frac{( x ^{3} + 20 x ^{2} + 8 )}{x + 20} d x

What is the integral from 0 to pi/2 of (5cos^2(x)) ?
The integral from 0 to pi/2 of (5cos^2(x)) is (5pi)/4