integral from-1 to 3 of (2x^2-x+3)^2

해법

\int_{- 1}^{3} (2 x^{2} - x + 3)^{2} d x

\frac{3728}{15}

십진법

248.53333 \dots

솔루션 단계

\int_{- 1}^{3} (2 x^{2} - x + 3)^{2} d x

(2 x^{2} - x + 3)^{2}

확대한다:

4 x^{4} - 4 x^{3} + 13 x^{2} - 6 x + 9

= \int_{- 1}^{3} 4 x^{4} - 4 x^{3} + 13 x^{2} - 6 x + 9 d x

합계 규칙 적용:

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

= \int_{- 1}^{3} 4 x^{4} d x - \int_{- 1}^{3} 4 x^{3} d x + \int_{- 1}^{3} 13 x^{2} d x - \int_{- 1}^{3} 6 x d x + \int_{- 1}^{3} 9 d x

\int_{- 1}^{3} 4 x^{4} d x = \frac{976}{5}

\int_{- 1}^{3} 4 x^{3} d x = 80

\int_{- 1}^{3} 13 x^{2} d x = \frac{364}{3}

\int_{- 1}^{3} 6 x d x = 24

\int_{- 1}^{3} 9 d x = 36

= \frac{976}{5} - 80 + \frac{364}{3} - 24 + 36

\frac{976}{5} - 80 + \frac{364}{3} - 24 + 36

간소화하다 :

\frac{3728}{15}

= \frac{3728}{15}