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Mathematics Senior High

数3の積分(置き換え)についてです これの(2)で√2-1=t で置き換えるとインテグラルを外した後に積分定数cにダッシュをつけてc´ -2=cとしているのはどうしてですか?

Think 例題140 置換積分法 (1) 次の不定積分を求めよ. (1) Sx(2x-1) dx 「考え方 解答 S dx = 1/2*1). より dt よって, 805- (Biel (1) 展開するのではなく, 2x-1=t とおいて考える. (2)√x=tとおく(√x-1=t とおいてもよい) C は積分定数とする. (1) 2x-1=t とおくと, t+1 x=- mm²n =dt dx= 168 (2)√x=t とおくと, dx -=2t より, dt よって, min t+1 Sx (2x - 1)³dx=S1-11 2 2dt -t°(6t +7) +C= 1 168 = ¼/S (tº +t³) dt = - t ³)dt = 1 + 1 € + 1 + 1 + + C 47 46 (2) x=t2 dx=2tdt S√/₁₁²_₁dx=S₁²₁ · ²tdt ~ (別解) x-1=t とおくと, dx -2t+2 より, dt 1 Sdx 1 2 置換積分法と部分積分法 309 -(2x-1)(12x+1)+C [2(t-1)+2 dt = √(2 + ₁ 2²₁) dt t-1 =2t+2log|t-1|+C=2√x+log(√x-1)'+C -dx x = t2+2t+1 KATAL =2√x+10g(√x-1)+C dx=(2t+2)dt 1200=1 A nie Sxdx=Sz(2x+2)at=S(2+2)at =2t+2log|t|+C'′=2(√x-1)+210g|√x-1|+C′ **** 12th 両辺をtで微分する. RED3 12dt を微分形式と いう. (p.307 参照) dx に 1/2dt を代入す る。 最後はxの式に戻す. m mmmmmmmmm 2tdt を微分形式と いう. (p.307 参照) dx に 2tdt を代入す る. fdx=log|x|+C 最後はxの式に戻す. x=g(t) とおくと (f(x)dx=Sf(g(t))g' (t)dt dx に (2t+2)dt を 代入する. C'′-2=Cとしている. 最後はxの式に戻す. 第5章

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English Senior High

なぜdに入るのが③なんですか?④ではないのですか?

Who was the first scientist? It wasn't Isaac Newton. Today, it is generally acknowledged that Newton never thought of himself as a scientist. He couldn't, for the word didn't exist in was not only a scientist, but the greatest scientist who ever lived, yet (Newton his time. Newton thought of himself as a "philosopher," a word that (a)dates back to the ancient Greek thinkers and that comes from Greek words (b)meaning "lover of wisdom." There are different kinds of wisdom we might love, of course. Some philosophers are concerned chiefly with the wisdom derived from the study of the world about us and the manner of its workings. The world { c ℗ about 2 be 3 can 4 referred 5 to 6 us as "nature," from the Latin word meaning “birth." Nature, in other words, is everything that has been created or that has come into being. Philosophers who deal primarily with nature are, therefore, "natural philosophers." Newton thought of himself as a natural philosopher, and the sort of thing he studied was natural philosophy. Thus, when he wrote the book (d) he carefully described his three laws of motion and his theory of universal gravitation—the greatest scientific book ever written-he called it (in Latin) Philosophiae Naturalis Principia Mathematica, which in English is The Mathematical Principles of Natural Philosophy. The Greek word for "natural" is physikos, which in English becomes physical. Natural philosophy might also be spoken of as "physical philosophy, which can be shortened to “physics.” on. Physics As natural philosophy grew and expanded, all kinds of special studies developed. People began to speak of chemistry, of geology, of physiology, and so was whatever was left over, so it didn't suit as a general overall word for natural philosophy. Yet you needed some such short word, for natural philosophy was a seven-syllable mouthful.

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English Junior High

🚨至急🚨 間違っている問題を教えてください!

5 次の対話文を読んで,あとの各問いに答えなさい。 Rika: Hi, Vanessa. Are you free after school tomorrow? Vanessa: Let me see.... I don't think I have anything special. Do you have any plans? Rika: 5 Vanessa: Rika: Vanessa: 10 Rika: I'm planning to have my birthday party tomorrow and I *want you to come. Actually my birthday is March 5, but.... That's today! Happy birthday, Rika! Thanks. But today is Thursday and I have my piano lesson going to have the party tomorrow. 3 That's a good idea, because we don't have any classes tomorrow afternoon. That means we can stay together longer. You're right. The party will start at two. for us. That's my favorite. That's my favorite, too. Oh, I can't wait. I'm also going to invite some of my friends in this class. Let's have a wonderful time together. Can I take my little sister with me? *I don't think she's ever been to such a party in 5 SV 0 Japan. Why not? I have a sister, too, so they can play together. want... to ~ ・・・に~してほしいと思う Vanessa: Rika: 15 Vanessa: Rika: 〔注〕 問5 問6 My mother is going to make chocolate cake I don't think she's ever been to 〜 彼女は今まで〜 へ行ったことがないと私は思う 問1 下線部①と同じ文型の文をア~オから1つ選び, 記号で答えなさい。 ア The news made her sad. イ He always buys me flowers. ウ She looks very nice in her new dress. エ Do you know the tall building over there? . オ Every morning he walks in the park before breakfast. 問2 下線部②とほぼ同じ内容を表すように, に適する語を[]内から選んで書きなさい。 any every all〕 Thursday [ some every 問3 ヴァネッサ (Vanessa) が下線部 ③ のように思った理由を日本語で答えるとき, ()の部分を補いなさい。 (金曜日の午後は2人とも予定がない 午後は2人と から。 問4 下線部④とほぼ同じ内容を表すように, My mother is going to make に適する語を書きなさい。 us 下線部⑤が第何文型であるかを答えなさい。 on Thursdays. So I'm 本文の内容と合うように,次の問いに英文で答えなさい。 What is Rika and Vanessa's favorite? a big chocolate cake. chacolate cake it 〔エ〕 第〔3〕 文型

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