integral from-2 to 3 of (4x^2+8)-(3x+2)

解答

\int_{- 2}^{3} (4 x^{2} + 8) - (3 x + 2) d x

\frac{415}{6}

十进制

69.16666 \dots

求解步骤

\int_{- 2}^{3} 4 x^{2} + 8 - (3 x + 2) d x

化简

= \int_{- 2}^{3} 4 x^{2} - 3 x + 6 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_{- 2}^{3} 4 x^{2} d x - \int_{- 2}^{3} 3 x d x + \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} 4 x^{2} d x = \frac{140}{3}

\int_{- 2}^{3} 3 x d x = \frac{15}{2}

\int_{- 2}^{3} 6 d x = 30

= \frac{140}{3} - \frac{15}{2} + 30

化简

\frac{140}{3} - \frac{15}{2} + 30 : \frac{415}{6}

= \frac{415}{6}

\int 7 x^{5} d x

\frac{d}{d x} (4 \cdot (x^{2} + 3 x))

\frac{d}{d x} (4 sec^{2} (2 x))

\int \frac{( 1 - t ) ^{2}}{t} d t

\frac{d}{d l} (2 π \frac{l}{9.8})