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지난 기출 AP 문제들을 다뤄보자는 제안을 받았습니다.

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그리고 인터넷을 들어갔더니

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칼리지보드(AP 주최기관) 사이트, collegeboard.com에서

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실제 객관식 문제들은 찾을 수 없었지만

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주관식 문제는 찾을 수가 있었죠.

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그래서 이 문제는 사실

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2008년 AP Calculus

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.1번 문제입니다.

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그럼 이제 문제를 풀어보도록 하죠.

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솔직히 여러분이 주관식 문제를

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어떻게 해결하는지 이해하면

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객관식 문제는 무난할 거에요.

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왜냐 하면, 주관식 문제들 그 중에서도 특히

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마지막 부분들은 좀 어렵기 때문이죠.

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하여간, 이 문제를 한 번 풀어보도록 할게요.

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이 문제를 다 쓰기는 좀 번거로우니

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그냥 제가 읽을게요

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사실 collegeboard.com에 올라와 있는

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pdf 파일 일부분을 그냥 복사해서 붙여넣기 한 거에요

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그러니까 이 R을 y=sinπx

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그래프에 의해 둘러싸인 부분의 넓이라고 합시다

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여기에다 쓸게요

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이 위쪽에 있는 그래프는

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y=sinπx 그래프에요.

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그리고 이 아래쪽의 그래프는

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y=x^2-4x 그래프에요

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이 그래프가 아래쪽 그래프인지 어떻게 알았냐고요?

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이 그래프가 y=sinπx 인지 알고 있었기 때문이에요

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왜냐 하면, sin 그래프는 이런 모양이기 때문이죠

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이 그래프는 그렇게 생기지 않았잖아요, 그렇죠?

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sinπ=0 이고

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sin(0)=0, sin(2π)=0

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그러므로 이게 sinπx가 되는 거에요.

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어쨌든 문제에서 요구하는 건 두 그래프 사이의
부분의 넓이에요.

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이 문제는 여러분이 정적분을 할 줄
아는 지 테스트 하기 위한

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간단한 문제에요

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문제에서 R의 넓이를 구하라고 하고 있어요

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어떻게 하면 될까요?

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정적분 계산이 필요하다는 걸 눈치 채셨겠죠?

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그러면 해 봅시다.

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정적분을 취할 거니까

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이 넓이는

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-제 글씨가 잘 보이시나요?

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정적분 식을 계산한 것과 같아요.

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여기서 x 값이 뭐죠?

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x=0 에서부터

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x=2 까지를

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계산하면 되겠네요

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앗!

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그러면 우리가 더할 이 직사각형 중의

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하나의 넓이가

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dx라고 합시다

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이 직사각형의 높이는 어떻게 되나요?

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높이는 위의 함숫값에서

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아래 합숫값을 뺀 것과 같겠죠.

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그러면 핵심은 우리가 이 직사각형을

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전부 다 더할 때 -잠깐만요 펜 색을 좀

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바꿀게요- 사각형의 높이는

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(윗쪽 함수) - (아래쪽 함수) 가 될거에요.

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그러면 높이는

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