całka iterowana do spr
: 28 gru 2011, 22:55
\(\int_{0}^{1}dx \int_{x^3}^{x^2} \frac{y}{x^2}dy\)
liczę tak:
\(\int_{0}^{1}dx \int_{x^3}^{x^2} \frac{y}{x^2}dy = \int_{0}^{1} \frac{1}{x^2}dx \int_{x^3}^{x^2} y dy= \int_{0}^{1} \frac{1}{x^2} \left[ \frac{y^2}{2} \right]_{x^3}^{x^2} dx= \int_{0}^{1} \frac{1}{x^2}\left( \frac{x^4-x^6}{2} \right)dx= \int_{0}^{1} \frac{x^2}{2}- \frac{x^4}{2}dx=\left[ \frac{x^3}{6}- \frac{x^5}{10} \right]_0^1= \frac{1}{6}- \frac{1}{10}= \frac{1}{15}\)
czy ktoś mógłby to sprawdzić?
liczę tak:
\(\int_{0}^{1}dx \int_{x^3}^{x^2} \frac{y}{x^2}dy = \int_{0}^{1} \frac{1}{x^2}dx \int_{x^3}^{x^2} y dy= \int_{0}^{1} \frac{1}{x^2} \left[ \frac{y^2}{2} \right]_{x^3}^{x^2} dx= \int_{0}^{1} \frac{1}{x^2}\left( \frac{x^4-x^6}{2} \right)dx= \int_{0}^{1} \frac{x^2}{2}- \frac{x^4}{2}dx=\left[ \frac{x^3}{6}- \frac{x^5}{10} \right]_0^1= \frac{1}{6}- \frac{1}{10}= \frac{1}{15}\)
czy ktoś mógłby to sprawdzić?