区分求積法（リーマン和）
分割数
n
を増やすと、長方形の面積の和が定積分の値に収束する様子を見ることができます。
関数
f(x) = x² [0, 2]
f(x) = x³ [0, 2]
f(x) = x⁴ [0, 1]
f(x) = 1 − x² [0, 1]
f(x) = x(1−x) [0, 1]
f(x) = 4x(1−x) [0, 1]
f(x) = (x−1)² [0, 2]
f(x) = x³ − x [−1, 1]（符号変化）
f(x) = sin x [0, π]
f(x) = cos x [0, π/2]
f(x) = sin²x [0, π]
f(x) = cos²x [0, π/2]
f(x) = sin x · cos x [0, π/2]
f(x) = sin 2x [0, π/2]
f(x) = |sin x| [0, 2π]
f(x) = tan x [0, π/4]
f(x) = sec x [0, π/4]
f(x) = csc x [π/4, π/2]
f(x) = cot x [π/4, π/2]
f(x) = sec²x [0, π/4]
f(x) = x sin x [0, π]（部分積分）
f(x) = e⁻ˣ sin x [0, π]（減衰曲線）
f(x) = sinh x [0, 1]
f(x) = cosh x [0, 1]
f(x) = sinh²x [0, 1]
f(x) = cosh²x [0, 1]
f(x) = sinh x · cosh x [0, 1]
f(x) = tanh x [0, 1]
f(x) = sech x [0, 1]
f(x) = csch x [1, 2]
f(x) = coth x [1, 2]
f(x) = eˣ [0, 1]
f(x) = e⁻ˣ [0, 1]
f(x) = 2ˣ [0, 1]
f(x) = e⁻ˣ² [0, 1]（ガウス）
f(x) = x · eˣ [0, 1]（部分積分）
f(x) = ln x [1, e]
f(x) = ln(1+x) [0, 1]
f(x) = x · ln x [1, e]
f(x) = 1/x [1, e]
f(x) = x² eˣ [0, 1]
f(x) = x e⁻ˣ [0, 1]
f(x) = e^(1/x) [1, 2]
f(x) = xˣ [0, 1]（Sophomore's dream）
f(x) = (ln x)/x [1, e]
f(x) = x/(ln x) [e, e²]
f(x) = arctan x [0, 1]
f(x) = arcsin x [0, 1]
f(x) = 1/(1+x²) [0, 1]
f(x) = 1/(x+1) [0, 1]
f(x) = x/(1+x²) [0, 1]
f(x) = √x [0, 1]
f(x) = √(1−x²) [0, 1]（四分円）
f(x) = √(4−x²) [0, 2]（半径2の四分円）
f(x) = x²/(x−1) [2, 3]
f(x) = x³/(x²−1) [2, 3]
f(x) = (x³+1)/x [1, 2]
f(x) = x + √(1−x²) [−1, 1]
f(x) = 2x + √(x²−1) [1, 2]
f(x) = |x − 1| [0, 2]
f(x) = floor(x) [0, 4]（階段関数）
f(x) = x − floor(x) [0, 4]（小数部分）
f(x) = sgn(x) [−1, 1]（符号関数）
f(x) = sin(1/x) [0.05, 1]（振動）
分割数 n
1
リーマン和 S
n
—
厳密値 ∫ f dx
—
誤差
—