a_{10} = S_{10} - S_9 = 230 - 189 = 41

Tue, 05 May 2026 01:12:37 +0000

Understanding the Area Under the Curve: A₁₀ = S₁₀ − S₉ = 230 − 189 = 41 in Mathematics When studying calculus or physics, one essential concept is the area under a curve, often represented mathematically as definite integrals. A common expression in this context is A₁₀ = S₁₀ − S₉, where Sₙ denotes the area under a function—or more precisely, the accumulated value of a function from one point to another—between successive intervals. This article explains what A₁₀ = 230 − 189 = 41 means, how to compute it, and why it’s a foundational example in mathematical and applied sciences. ### What Does A₁₀ = S₁₀ − S₉ Represent? In calculus, Sₙ typically represents the integral of a function f(x) from 0 to n (i.e., Sₙ = ∫₀ⁿ f(x) dx). Therefore, the difference A₁₀ = S₁₀ − S₉ calculates the total area under the curve of f(x) over the interval from x = 9 to x = 10: