Ngô Quốc Anh

October 11, 2007

Tính tích phân xác định bằng cách dùng ý nghĩa hình học của nó

Filed under: Các Bài Tập Nhỏ, Giải Tích 2 — Ngô Quốc Anh @ 0:40

Calculate

\displaystyle\int_0^1\left(\sqrt [5]{1 - x^9}-\sqrt [9]{1 - x^5}\right) dx.

Solution. Let S be the set of points (x, y) in the first quadrant such that x^9 + y^5 \leq 1. We can interpret

\displaystyle\int_0^1 \sqrt[5]{1 - x^9}dx

as the area of S. Similarly, we can interpret

\displaystyle\int_0^1 \sqrt[9]{1 - y^5}dy

as the area of S. So the answer is \boxed{0}.

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