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Mathematics Senior High

積分の問題です。 黄色マーカーで引いたところの解説をお願いします

基礎問 220 第6章 積分法 120 回転体の体積 (V) 曲線 y= (vi-va) (x≧0, a>0) について,次の問いに答えよ. (1) この曲線のグラフをかけ. (2) この曲線と y=α によって囲まれた部分を直線y=a のまわりに 1回転してできる体積を求めよ. (1) 75 をもう一度読みかえしてみましょう. 今回は, 極値 を求める必要がありますから, y' は因数分解することになります. .......... それならば,このまま微分した方がよいでしょう. (2)今まで学んだ回転体の体積は、回転軸がx軸かy軸でした。今回は、y=a です.いったいどのように考えればよいのでしょう。 目標は, 「回転軸をx 軸に重ねる」ことです. 精講 (1) x>0 のとき y'=2(√x - √a). (√x - √a)=x^² (√x - √a) 1-√a =1- 解答 x→+0 ->0 I √a 2x√x よって, グラフは下に凸で,増減は表のようにな り, limy'=-8, limy =∞ よりグラフは右図. 218 0 ... a y' 4 a 0 + V 20 (2) 曲線と直線y=α の交点のx座標は (√x - √a)² = a√x - √√a = ± √a √x=0, 2√a :: x=0, 4a 8/4 a 10 x=0のとき、 y'の分母= 0 となるので a 注 limy' を調べているのは, y' が x=0 で定義されていない, すな x→+0 わち, 微分可能でないからです. このことは, グラフにおいて点 (0, a) でy軸に接するようにかかれている部分でいかされています。 IC 求める体積Vは〈図Ⅰ>の斜線部分を直線y=a のまわりに回転させ! た立体の体積だから、この図形を軸の正方 向に-4だけ平行移動した <図II〉の斜線部 (141) 分をx軸のまわりに回転すればよい。 "". V=1 = πf^^{(√x - √a)²-a³dx = n₁²(x-²√a √x)²dx 演習問題 120 *4α = nſ₁² (x² − 4√a x² + 4ax) dx ポイント x³ 8√a 5 5 8.25 = π[3³ = nα² (43 4³ 242 15 = ・+2・4 5+2.4²) -ла³(10-24+15) -x²+2ax² πa³ 14g YA 0 a 221 32 15 数学ⅡI・B48 ポイントによれば, 平行移動の公式は次の通り。 注 y=(√x-a-a y=f(x) をx軸の正方向にp,y軸の正方向に qだけ 平行移動すると, y-q=f(x-p) となる. Anx 回転軸がx軸やy軸でないとき, 平行移動して回転軸を軸や軸に重ねる (1411) 4 エ y=cosx のグラフと, 点 (0, 1) と点 (2m, 1 ) を結ぶ線分で囲ま れた領域を直線y=1のまわりに1回転してできる立体の体積V を求めよ. 79 第6章

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English Senior High

日本語訳をお願いしたいです!!お願いします

次の英文を読んで、設問に答えなさい。 Everybody wants to eat delicious and safe food. However, exposure to different cultures reveals 2 how people's attitudes towards food safety and taste are not all innate or biological. Assumptions and practices regarding the preparation and presentation of food highlight the influence of culture on what and how people eat. For example, in one culture, some kinds of fresh ingredients might be considered edible (a), that is, without any kind of preparation like washing, peeling or heating. Yet in another culture, the same foodstuff may require some kind of preparation before it can be eaten. It is often difficult for people from the same culture to view such activities and beliefs objectively, and so witnessing the food practices of other cultures can be surprising. Sashimi is a great example of this. While sashimi may be the result of several steps of preparation from cleaning and cutting, to a particular style of presentation - heating is not one of these steps. (2)Japanese consumers take it for granted Cultures, the conventional belief may be that real and fish require some sort of cooking, such as baking or frying, (3) in order (b) them to be considered edible. In these cultures, sashimi is not thought of as raw, delicious and safe to eat, but rather as uncooked, and therefore possibly unsafe to eat, regardless of how it may taste. Fresh chicken eggs are another raw foodstuff commonly eaten in Japan — as a topping for rice, or as a dipping sauce for sukiyaki, for example but most people in the UK or the USA believe that chicken eggs require some kind of heating before they are fit for human consumption. However, the ways in which people from other cultural backgrounds eat certain foods might be considered equally unconventional by many Japanese. For example, few Japanese would eat the skin of apples or grapes. In this case, the difference involved in the preparation of the food is not the use of heat, but the removal of part of the foodstuff. People in much of the world eat apples and grapes without peeling them. A European might think, What could be more healthy and delicious than picking an apple from the tree and eating it?' But this way of thinking is not shared by a large number of Japanese. (4) It is clear that different cultures have different conventions regarding the preparation of particular foods, and different beliefs about what is considered delicious. However, there is no question that some common food preparation practices - or sometimes a lack of certain food preparation processes - are unsafe from a scientific point of view. However delicious they may be, raw meat and fish can contain the eggs of harmful parasites like tapeworms, which are often undetectable. If chicken eggs are not properly stored, and are left unconsumed for a long time, they can easily produce bacteria like salmonella. The poisoning caused by salmonella does not usually require hospitalization, but it can be very dangerous for young children and elderly people. In addition, while eating the skin of apples and grapes may be a good source of dietary fiber, one also runs the risk of consuming insecticides, the poisons that are used to protect many non-organically farmed fruits from insects. So, while there may be 'no accounting for taste' beyond culture, safety is a different issue, and (5) we should always be aware of the risks involved with culturally accepted methods of food production and consumption. 問1 下線部 (1)で,空欄 ( a )に入る最も適切な語句を, (A)~(D)から選び, 記号で答えなさい。 (A) as is clear (B) as is fresh (C) as they are (D) as unclean 問2 問3 問4 問5 下線部(2)を日本語に訳しなさい。 下線部 (3)の空欄(b)に入る語(1語) を書きなさい。 下線部(4) を日本語に訳しなさい。 下線部 (5)の理由として最も適切なものを, (A)~(D) から選び,記号で答えなさい。 (A) Eating raw chicken eggs or unpeeled fruits can be dangerous in certain conditions because of harmful bacteria or pesticides. (B) Eating unpeeled apples or grapes may cause weight gain. (C) Only young children and elderly people are vulnerable to particular bacteria. (D) Beliefs about what is considered delicious actually come from better understanding of food preparation. 問6 本文の内容と一致するものを, (A)~(G)から3つ選び,記号で答えなさい。 (A) By food preparation processes, the author exclusively means the use of heat. (B) Culturally established ways of consuming food may conflict with scientific principles of food safety. (C) In some food cultures outside Japan, fish in its raw state is not categorized as an edible foodstuff. (D) People having little contact with other cultures tend to view their own food-related conventions as natural and standard. (E) Repeated exercise is required for the mastery of any food preparation. (F) Instinct alone determines what and how people eat. (G) All cultures around the world consider it natural to eat unpeeled fruit.

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Mathematics Senior High

⑴で、どうして dy=1/e e y/e dyとならないのですか?

形の面積 65-267, を果たす。 --g(x)}dx -in 2x x 2π I は, x)の符号 よい。 曲線x=g(y) とy軸の間の面積 基本例題 257 次の曲線と直線で囲まれた部分の面積Sを求めよ。 yelogx, y=-1, y=2e,y軸 y=-cosx (0≤x≤n), y=-1/2, y=-1₁ でもよい。 解答 (1) y=elogx から -1≤y≤2e CHIC XU •2e 2e kot S=S² e dy=[e-e = 1² ₁ まず、曲線の概形をかき, 曲線と直線や座標軸との交点を調べる。 (1) yelogxをxについて解き,yで積分するとよい。 ・・・xについての積分で面積を求めるよりも、計算がらくになる。 (2)(1) と同じように考えても,高校数学の範囲では y=-cosx を x=g(y) の形にはできない。 そこで置換積分法を利用する。 (1),(2) ともに 別解 のような, 長方形の面積から引く方法 =e.e² - e•e== 3=e³-e¹-1/ (2) y=-cosx75 よっ x=ee π y dy=sinxdx xsinxdx -|-xcosx}"+f" cosxdx COS X π - - - - - - (-1/2) + 5 - 12/12 3 +0= + TC 2 sinx yA 2e e S 練習 ③257 (1) x=y2-2y-3, y=-x-1 (2)y= 1 √x y=1, y= -1 y軸 2' 2 8. ya 1 1 2. O 17 y軸 y 2 2 113 π e² 1 2 2e+1 Y+WA S p.424 基本事項 ③ 3 x=ee 102 ↑ SEX 00000 2 T2 y=–cost π 次の曲線と直線で囲まれた部分の面積Sを求めよ。 4703 π y x d =2e3+e² || 重要 263 x=g(y) (1) の 別解 (長方形の面積か ら引く方法) S=e²(2e+1) TC 2 常に g(y)≥0 s=g(y)dy -S4(elog.x+1)dx -[e(xlogx-x)+x] + =e³-e¹-² (2) の 別解 (上と同じ方法) S = ²/3 x ² ( 7²2 +²2²) S= 427 T cosx+ 1/1/2)dx Hot CO 8章 38 面積 38 Op.440 EX213

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