integral from-4 to 4 of 4(16-x^2)

解答

\int_{- 4}^{4} 4 (16 - x^{2}) d x

\frac{1024}{3}

十进制

341.33333 \dots

求解步骤

\int_{- 4}^{4} 4 (16 - x^{2}) d x

提出常数:

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

= 4 \cdot \int_{- 4}^{4} 16 - x^{2} 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

= 4 (\int_{- 4}^{4} 16 d x - \int_{- 4}^{4} x^{2} d x)

\int_{- 4}^{4} 16 d x = 128

\int_{- 4}^{4} x^{2} d x = \frac{128}{3}

= 4 (128 - \frac{128}{3})

化简

4 (128 - \frac{128}{3}) : \frac{1024}{3}

= \frac{1024}{3}

d er i v a t i v e 2 x^{3} - 5

x \to - 1 - lim (\frac{1}{x - 1} + e^{x})

\frac{d}{d t} (3 t)

\int \frac{( x ^{2} + 2 x + 1 )}{( x + 3 )} d x

\frac{d y}{d t} = y^{2} - 4