integral from 1 to 2 of x^3+3x^2-4x

해법

\int_{1}^{2} x^{3} + 3 x^{2} - 4 x d x

\frac{19}{4}

솔루션 단계

\int_{1}^{2} x^{3} + 3 x^{2} - 4 x 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}^{2} x^{3} d x + \int_{1}^{2} 3 x^{2} d x - \int_{1}^{2} 4 x d x

\int_{1}^{2} x^{3} d x = \frac{15}{4}

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 4 x d x = 6

= \frac{15}{4} + 7 - 6

\frac{15}{4} + 7 - 6

간소화하다 :

\frac{19}{4}

= \frac{19}{4}