これって半角の公式使わないと出来ないですか？

半角 dx (8) 1+cosx

答えが公開されていないので、わかる方に答え合わせお願いしたいです😭🙇‍♀️

IV. (1) から (5) の各問いにおいて, 1.~6. の語句を並べ替えて空所を補い, 最も適当な英文 を完成させなさい。 解答は解答用紙2枚目 (記述式) の所定の解答欄に, (A)と (B)に入る語句の番号を記入すること｡ (1) I like English because I feel like a different person when I am speaking it. Although it is difficult to speak well, I enjoy the challenge. Someday I hope ( ) (A) ( ) ( ) (B) ( ) in English. 1. even dream 5. the level 1. young people 2. acquire 5. provide (2) Volunteering is a good thing because it teaches young adults valuable lessons about life. For one, it teaches them that charity is an investment. By helping others you also help yourself. Volunteering can also ( ) ( A ) ( ) ( ) ( B ) ) practical experience. 1. health 5. to 2. where 6. I can. 1. lacking 5. found of what roles physical activity, exercise and nutrition play. neither prevent nor manage disease. 6. an opportunity (3) There are at least four kinds of education people should get when they are young: physical education, moral education, intellectual education and nutrition education. Those ( ) (A) ( ) ( ) ( B ) ( ) have an understanding Without them we can Q wear 5. we 3. reach 2. in 6. interested 3. with 2. and 6. more (4) E-mail and other SNS applications are now the primary means of communication in much of the world. While this is certainly one form of socialization, it seems to be replacing social interaction in person. As a result, more ( ) ( A ) ( ) ( ) ( B ) ( ) in the social skills and values that are essential to their integration into a group or community. 2 clothes 6. to 4. to 3. need 4. to 3. are (5) Presumably fashion reflects our personalities. The ( ) ( A ) ( :) ( ^_-) (B) ( ) who and what we are. Many people wear clothes to try and fit in, some to impress others, and some just wear the clothes they own. Your clothing is a reflection of who you are one way or another. 3. like 4. mental or physical 4. people 4. show Basic Elements for Communication (t, 2019 4), 7, 35, 59, 71, 87 ( 改変)

この問題、and more people are lacking found で合ってますか？💦 あってたらなぜlackingの後に動詞が続くのか教えて欲しいです😭

(4) E-mail and other SNS applications are now the primary means of communication in much of the world. While this is certainly one form of socialization, it seems to be replacing social interaction in person. As a result, more ( ) ( A ) ( ) ) ( B ) ( ) in the social skills and values that are essential to their integration into a group or community. 1. lacking 5. found 2. and 6. more 3. are 4. people

この文の緑のマーカー引いてるところの、訳と構造を教えて欲しいです！特にcrimes for which のところがなぜそうなるかわからないです

and have 2 R not Advances in technology/over the past 200 years have been remarkable ght us many benefits/However, the integration of technology Into society has always been smooth/ The first industrial revolution began in Britain in the late 18th century/Machines developed at the time/could make clothes much more efficiently (1) 14 easily and cheaply than before. Even so not everyone felt happy about this at first. Groups of skilled weavers and textile machine operators known as Luddites feared 労働運動 that their jobs would be taken away/They began/a labor movem ement in order to protest and resist the widespread use of the new technology by factory owners. Their protest actions included destroying machines crimes for which some Luddites were killed by authorities. ようたい CO ↑ To Cut 27. 減速する we now know these technological advances did not/slow down. Over time, they became widely accepted and appreciated. Before long, other innovations like the steam engine were powering heavy machinery across Europe and beyond. The second industrial revolution, toward the end of the 1800s, brought the gasoline engine and the s use of electricity. The third industrial revolution, in the late 20th century, produced computers as well as digital technologies and communications. And, recently, experts have declared that developments in artificial intelligence (AI) and advanced robotics have led us into the fourth industrial revolution. Even today, however, we hear warnings about the potentially harmful effects of (2) contemporary technologies. Some observers claim that the latest AI inventions could have negative impacts on workers, businesses, and society as a whole. The main concern, as in past eras, is that machines will replace humans in the workplace. Thes- observers suggest that a large number of occupations might be lost to AI and robot in the next few years. Taxi and truck drivers, cleaners, and factory workers are amon those considered to be at risk. The fear is even expressed that the AI revolution might lead to mass unemploymen According to some experts, up to 800 million jobs could be lost globally by 203 Moreover, the workers who will lose their jobs to machines are likely to be those wit ewer skills and less education, increasing the gap between rich and poor. Some peop believe that this will create social conflict and instability. do not necessarily need to take such a negative outl

四角で囲った部分がよく分からないので教えてほしいです！

(1) 15xs/it と異なる結果 tan 6 18 0= To ないからで､この 応は誤りである。 x = atandについ (1) ri すると 分解する。 FA として分する 基本例題 231 偶関数,奇関数の定積分 次の定積分を求めよ。 (1) ではaは定数とする。 (1) ²√a²+x² 解答 (1) f(x)=√a²+x² x³ √²+x² f(-x) == よって, -dx 指針 定積分の計算は、偶関数・奇関数に分けて考える。① Sof(x)dx=2Sf(x)dx 関数 f(x)=f(x) (y軸対称) 奇関数 f(-x)=-f(x) (原点対称) S° f(x)dx=0 CHART S゜の扱い 偶関数は 2 , 奇関数は 0 したがって ここで よって とすると (-x)³ √a²+(-x)² 5²₁ S -a 関数であるから ARCH X(2) S(2sinx+cosx)dx エー J √a²+x² x3 ²√√a²+x² (2) (2sinx+cosx) |— qua =8sin3x+12sinxcosx+6sinxcosx+cos3x -dx=0 -= -f(x) sinx は奇関数 COS x は偶関数であるから, sin x は奇数 sin' x cos x は偶関数 sin x cos' x は奇関数 COS' x は偶関数。 π (与式)=2(12sin'xcosx+cosx)dx 12sin'xcosx+cosx=(12sin²x+cos'x) cosx =(12sinx+1−sin’x)cosx =(11 sin²x+1) cos x (与式)=2 (11sin x+1)(sinx)'dx -sin®x+sing] =211/2 sin = 28 3 nias 2 p.380 基本事項 ② 練習 次の定積分を求めよ。 (2) では qは定数とする。 ②231 (1) S(2sint+3cost)'dt (3) S (cosx+ x sinx)dx ←計算不要。 +³ (a>0) ya O 積分区間 が半分。 kin SCORD (2) S²₂x√√a²-x² dx a 被積分関数が奇関数である ことがわかれば, 積分を計 算する必要はない。 x 奇数×奇関数=偶関数 奇関数×偶関数 = 奇関数 偶関数×偶関数=偶関数 公式を用いて次数を下げて もよいが,この問題では f(■)の発見の方針で 進めた方が早い。 20 sinx=uとおくと cosxdx = du 左の定積分 は25%(11²+1)du 35 7章 4定積分の置換積分法・部分積分法 34

定積分で面積が求まるのはどうしてですか？

この積分なんですけど、なんで、青い線で書かれた発想が思い浮かぶのか教えてください🙏

de -698-13 m ド を t-41

(2)で線がある所が分かりません。 計算を楽にするために奇数乗偶数乗で分けているのだと思うんですが吹き出しの部分の式が0など綺麗な数になるのは計算しないとわからないと思いどういう思考回路で解いているのか分かりません。

の定積分の計算をせよ- 代デアーな ヴージなキト(デーggr 3 DcデーたCiDape まじおう3 っ eーのの 2生な所や) の 記@+DG-Dー TOG-Dez (GtDe=Dのキ Gr De Derる) CrtDGe-D 定本分の性買⑤ ュ っーー1)gzス雪細が0に因じと半人

解き方、答えが違うんですけど、なんでこの求め方だとダメなんですか？

165 放物閑 ッニァ*ー3ヶ3 と 了もor。 面積Sを求めよ。 5r+7 で半まれた知人のの デー3ァー3ニーァ*二57 一 2**ー8z-10=0 2(zヶー5)(>+1)=0 >=-s よって, 求める面積Sは図の色の部分 5ニー2有なー5(z+Dgz ETm ニーなTi-6(<+Dgz <思 交半の確認 一利etD-eh半. ーーす6ー3.9)-2"=o 県の和分をくくるのがコツ | 図は上下関係を確認するための ものですか ょうに, きちん 7軸までかく必要はありません

ウ を求めるところなんですが、緑の線の所はどのように導かれたのですか？1行前から途中式を教えてください！

ーー 0 以上の整数ヶ に対して ィー/ me 』 A 且 とする。このとき, 70 = である。 また, し は 3. …) 、 を満たす。 人 は。 積分記号を用いずに答えよ。)