What is the integral from 0 to 1/2 of xcos(pi)x ?

The integral from 0 to 1/2 of xcos(pi)x is -1/24

Popular >

integral from 0 to 1/2 of xcos(pi)x

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

- \frac{1}{24}

Decimal Notation

- 0.04166 \dots

Solution steps

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

Take the constant out:

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

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

cos (π) = - 1

= (- 1) \cdot \int_{0}^{\frac{1}{2}} xx d x

Simplify

xx : x^{2}

= (- 1) \cdot \int_{0}^{\frac{1}{2}} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{\frac{1}{2}}

= (- 1) [\frac{x ^{3}}{3}]_{0}^{\frac{1}{2}}

Simplify

= - [\frac{x ^{3}}{3}]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{1}{24}

= - \frac{1}{24}

\int_{0}^{1.75} 600 x d x

x \to 0 lim (e^{\frac{8}{x}})

f (y) = \frac{A}{y ^{9}} + B e^{y}

x \to 2 - lim (\frac{3}{x - 2})

\frac{d}{d x} ((cos (x))^{2} + sin (x^{2}))

What is the integral from 0 to 1/2 of xcos(pi)x ?
The integral from 0 to 1/2 of xcos(pi)x is -1/24