"파이 π는 무리수이다"의 두 판 사이의 차이

2010년 7월 12일 (월) 20:11 판

\(\int_0^1 x \sin \pi x\,dx = \frac{1}{\pi}\)

\(\int_0^1x^2 \sin \pi x\,dx = \frac{\pi^2-4}{\pi^3}\)

\(\int_0^1x^3 \sin \pi x\,dx = \frac{\pi^2-6}{\pi^3}\)

\(\int_0^1x^4 \sin \pi x\,dx = \frac{48-12 \pi^2+\pi^4}{\pi^5}\)

\(\int_0^1x^5 \sin \pi x\,dx = \frac{120-20 \pi^2+\pi^4}{\pi^5}\)

\(\int_0^1x^6 \sin \pi x\,dx = \frac{-1440+360\pi^2-30 \pi^4+\pi^6}{\pi^7}\)

@@ 12번째 줄: / 12번째 줄: @@
 <h5>관찰1</h5>
+<math>\int_0^1 x \sin \pi x\,dx = \frac{1}{\pi}</math>
+<math>\int_0^1x^2 \sin \pi x\,dx = \frac{\pi^2-4}{\pi^3}</math>
 <math>\int_0^1x^3 \sin \pi x\,dx = \frac{\pi^2-6}{\pi^3}</math>
-<math>\int_0^1x^3 \sin \pi x\,dx = \frac{\pi^2-6}{\pi^3}</math>
+<math>\int_0^1x^4 \sin \pi x\,dx = \frac{48-12 \pi^2+\pi^4}{\pi^5}</math>
+<math>\int_0^1x^5 \sin \pi x\,dx = \frac{120-20 \pi^2+\pi^4}{\pi^5}</math>
+<math>\int_0^1x^6 \sin \pi x\,dx = \frac{-1440+360\pi^2-30 \pi^4+\pi^6}{\pi^7}</math>
-<math>\int_0^1x^3 \sin \pi x\,dx = \frac{\pi^2-6}{\pi^3}</math>