【微分積分】4-1-1 定積分の定義｜問題集
1.次の定積分を求めなさい。
(1)\(\displaystyle \int_a^b x^2dx\)
\(\displaystyle =\left[\frac{1}{3}x^3\right]_a^b\)
\(\displaystyle =\frac{1}{3}b^3-\frac{1}{3}a^3\)
\(\displaystyle =\frac{1}{3}(b^3-a^3)\)
\(\displaystyle =\frac{1}{3}b^3-\frac{1}{3}a^3\)
\(\displaystyle =\frac{1}{3}(b^3-a^3)\)
(2)\(\displaystyle \int_a^b x^3dx\)
\(\displaystyle =\left[\frac{1}{4}x^4\right]_a^b\)
\(\displaystyle =\frac{1}{4}b^4-\frac{1}{4}a^4\)
\(\displaystyle =\frac{1}{4}(b^4-a^4)\)
\(\displaystyle =\frac{1}{4}b^4-\frac{1}{4}a^4\)
\(\displaystyle =\frac{1}{4}(b^4-a^4)\)
(3)\(\displaystyle \int_a^b e^xdx\)
\(=[e^x]_a^b\)
\(=e^b-e^a\)
\(=e^b-e^a\)
次の学習に進もう！