부정적분 함수값

함수 $f \left( x \right) = x ^{2} - 2 x - 5$의 한 부정적분이 $F \left( x \right)$이므로 $F \left( x \right)$$\displaystyle = \int \left( x ^{2} - 2 x - 5 \right) dx$ $\displaystyle = \frac{1}{3} x ^{3} - x ^{2} - 5 x + C$ (단, $C$는 적분상수) $F \left( 0 \right) = 6$이므로 $C = 6$ $\displaystyle \therefore F \left( x \right) = \frac{1}{3} x ^{3} - x ^{2} - 5 x + 6$ $\therefore F \left( 3 \right)$$\displaystyle = \frac{1}{3} \times 3 ^{3} - 3 ^{2} - 5 \times 3 + 6$ $= 9 - 9 - 15 + 6$ $= - 9$