integral from-7 to 7 of 49-x^2

解答

\int_{- 7}^{7} 49 - x^{2} d x

\frac{1372}{3}

十进制

457.33333 \dots

求解步骤

\int_{- 7}^{7} 49 - 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

= \int_{- 7}^{7} 49 d x - \int_{- 7}^{7} x^{2} d x

\int_{- 7}^{7} 49 d x = 686

\int_{- 7}^{7} x^{2} d x = \frac{686}{3}

= 686 - \frac{686}{3}

化简

686 - \frac{686}{3} : \frac{1372}{3}

= \frac{1372}{3}

d er i v a t i v e - \frac{2}{5} x^{\frac{3}{4}}

\int_{1}^{6} \frac{5}{x ^{2}} d x

d er i v a t i v e f (x) = x^{4} - 6 x^{2} + 9

\frac{d}{d t} (in cos (t))

\int x^{4} 5^{x} d x