integral from 0 to 1 of cos^2(pix)

解答

\int_{0}^{1} cos^{2} (π x) d x

\frac{1}{2}

十进制

0.5

求解步骤

\int_{0}^{1} cos^{2} (π x) d x

使用三角恒等式改写

= \int_{0}^{1} 1 - sin^{2} (π x) d x

使用积分加法定则:

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

= \int_{0}^{1} 1 d x - \int_{0}^{1} sin^{2} (π x) d x

\int_{0}^{1} 1 d x = 1

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

= 1 - \frac{1}{2}

化简

1 - \frac{1}{2} : \frac{1}{2}

= \frac{1}{2}

\int \frac{2 - x}{x ^{2}} d x

\frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}})

\int 54 - 18 z - 6 z^{2} + 2 z^{3} d z

\int_{0}^{1} 2 x 5^{x} d x

d er i v a t i v e v^{\frac{3}{2}} (v + c e^{x})