Hi, there!
Triple-layer Osechi box reminds me of my mother’s New Year’s cooking,
which was so delicious that I used to eat all of the foods as quick as a
flash within a few days or so.
The New Year’s dish brought out the flavor of the selections, such as her-
ring roe, black beans, fish paste, and whatnot. It perfectly matched with
Ozouni, or soup containing rice cakes and vegetables. I am reminiscent
of my mother’s loving cooked foods and would feel family bondage on
that special occasion.
The word “Triple” feels robust flavor, which has naturally produced a chal-
lenging spirit for me to solve a triple integration word problem.
Evaluate \(\int_{3}^{4}\int_{0}^{5}\int_{2}^{1}5x^{2}y – 2z^{3}dzdydx\).
This problem doesn’t take an onerous task. All I have to do is integrate
following the given order, start with the inside integral, and work my
way out.
Here is the \(z\) integration.
\(\int_{3}^{4}\int_{0}^{5}\int_{2}^{1}5x^{2}y – 2z^{3}dzdydx\)
\(=\int_{3}^{4}\int_{0}^{5}(5x^{2}y – \frac{1}{2}z^{4})|_{2}^{1}dydx\)
\(=\int_{3}^{4}\int_{0}^{5}\frac{15}{2} – 5x^{2}ydydx\)
See to it that triple integration is just like double integration and all the
variables other than the one are considered to be constants. So, for the
\(z\) integration, the \(x\)’s and \(y\)’s are all considered to be constants.
Then, I’ll do the \(y\) integration.
\(\int_{3}^{4}\int_{0}^{5}\int_{2}^{1}5x^{2}y – 2z^{3}dzdydx\)
\(=\int_{3}^{4}(\frac{15}{2}y – \frac{5}{2}x^{2}y^{2})|_{0}^{5}dx\)
\(=\int_{3}^{4}\frac{75}{2} – \frac{125}{2}x^{2}dx\)
Finally, I’ll do the \(x\) integration.
\(\int_{3}^{4}\int_{0}^{5}\int_{2}^{1}5x^{2}y – 2z^{3}dzdydx\)
\(=(\frac{75}{2}x – \frac{125}{6}x^{3})|_{3}^{4}\)
\(=-\frac{2200}{3}\)
You might want to avoid “Triple delivery” in your presentation, for
“Triple” doesn’t always mean a value-added to your presentation.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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