integral de 0 a pi de pi^{25}sin^2(x)

Solução

\int_{0}^{π} π^{25} sin^{2} (x) d x

\frac{π ^{26}}{2}

Decimal

4215670845938.099

Passos da solução

\int_{0}^{π} π^{25} sin^{2} (x) d x

Remover a constante:

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

= π^{25} \cdot \int_{0}^{π} sin^{2} (x) d x

Reeecreva usando identidades trigonométricas

= π^{25} \cdot \int_{0}^{π} \frac{1 - cos ( 2 x )}{2} d x

Remover a constante:

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

= π^{25} \frac{1}{2} \cdot \int_{0}^{π} 1 - cos (2 x) d x

Aplicar a regra da soma:

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

= π^{25} \frac{1}{2} (\int_{0}^{π} 1 d x - \int_{0}^{π} cos (2 x) d x)

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (2 x) d x = 0

= π^{25} \frac{1}{2} (π - 0)

Simplificar

π^{25} \frac{1}{2} (π - 0) : \frac{π ^{26}}{2}

= \frac{π ^{26}}{2}

\int 1 d θ

\int_{0}^{9} 1 + x d x

n = 1 \sum \infty arctan (n^{2})

x \to \infty lim (5 \infty^{3} + \frac{1}{7})

x \to 0 lim (\frac{( 2 ^{x} - 2 ^{- x} )}{x})