定積分の計算問題です。 $\int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx$ を計算しなさい。解析学定積分積分計算2025/4/71. 問題の内容定積分の計算問題です。∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx\int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dxを計算しなさい。2. 解き方の手順まず、定積分の性質を利用して、積分範囲をまとめます。∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx\int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx=∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx= \int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx=∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx=∫−13(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx−∫−33(2x2−9x+11)dx= \int_{-1}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx=∫−13(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=∫−33(2x2−9x+11)dx−∫−33(2x2−9x+11)dx= \int_{-3}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx=∫−33(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=∫−3−1(2x2−9x+11)dx+∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx= \int_{-3}^{-1} (2x^2 - 9x + 11) dx + \int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx=∫−3−1(2x2−9x+11)dx+∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=∫−33(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=0= \int_{-3}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx = 0=∫−33(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=0別の方法として、∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx\int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx=∫−13(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx−∫−33(2x2−9x+11)dx= \int_{-1}^{3} (2x^2 - 9x + 11) dx + \int_{-3}^{-1} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx=∫−13(2x2−9x+11)dx+∫−3−1(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=∫−3−1(2x2−9x+11)dx+∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx= \int_{-3}^{-1} (2x^2 - 9x + 11) dx + \int_{-1}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx=∫−3−1(2x2−9x+11)dx+∫−13(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=∫−33(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=0= \int_{-3}^{3} (2x^2 - 9x + 11) dx - \int_{-3}^{3} (2x^2 - 9x + 11) dx = 0=∫−33(2x2−9x+11)dx−∫−33(2x2−9x+11)dx=03. 最終的な答え0