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受欢迎的微积分 >

integral from-pi to 0 of-3cos^2(x)sin(x)

解答

\int_{- π}^{0} - 3 cos^{2} (x) sin (x) d x

解答

2

求解步骤

\int_{- π}^{0} - 3 cos^{2} (x) sin (x) d x

提出常数:

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

= - 3 \cdot \int_{- π}^{0} cos^{2} (x) sin (x) d x

使用换元积分法

= - 3 \cdot \int_{- 1}^{1} - u^{2} d u

提出常数:

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

= - 3 (- \int_{- 1}^{1} u^{2} d u)

使用幂法则

= - 3 (- [\frac{u ^{3}}{3}]_{- 1}^{1})

化简

= 3 [\frac{u ^{3}}{3}]_{- 1}^{1}

带入上下限计算后得:

\frac{2}{3}

= 3 \cdot \frac{2}{3}

化简

= 2

作图

流行的例子

integral from-4 to 6 of |x|

\int_{- 4}^{6} ∣ x ∣ d x

integral from-2 to-1 of (x^2+1/(x^2))

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

integral from 1 to 4 of x^2ln(x)

\int_{1}^{4} x^{2} ln (x) d x

integral from 0 to 1 of (x^2-2x+5)

\int_{0}^{1} (x^{2} - 2 x + 5) d x

integral from 1 to x of e^{-t^2}

\int_{1}^{x} e^{- t^{2}} d t