Question 1
1 mark\( 0 \le x \le 4 \) の範囲において、曲線 \( y = x^2 - 4x + 6 \) と \( x \) 軸、および2直線 \( x = 0, x = 4 \) で囲まれた部分の面積を求めなさい。
Senior High School · Mathematics
Integration: Practice Questions
5 multiple-choice questions marked as you go, and 3 written questions with worked solutions. All on Integration.
8 questions16 marksFree, no account
Question 2
1 mark定積分 \( \int_{0}^{\pi/2} x \cos x dx \) の値を求めなさい。
Question 3
1 mark放物線 \( y = 4 - x^2 \) と直線 \( y = x + 2 \) で囲まれた部分の面積を求めなさい。
Question 4
1 mark曲線 \( y = \sin x \) \( (0 \leq x \leq \pi) \) と \( x \) 軸で囲まれた図形を、\( x \) 軸の周りに1回転させてできる回転体の体積を求めなさい。
Question 5
1 mark曲線 \( y = \sqrt{x} \) と直線 \( y = x \) で囲まれた部分の面積を求めなさい。
Question 6
2 marks不定積分 \( \int (3x^2 - 4x + 5) dx \) を求めなさい。
Write your answer out first, then check it against the worked solution.
Question 7
3 marks定積分 \( \int_{0}^{2} (3x^2 - 4x + 1) dx \) を計算しなさい。
Write your answer out first, then check it against the worked solution.
Question 8
6 marks曲線 \(y = x^3 - 3x^2 + 2\) 上の点 \(P(1, 0)\) における接線の方程式を求めなさい。また、この接線と曲線によって囲まれた部分の面積 \(S\) を定積分を用いて計算しなさい。
Write your answer out first, then check it against the worked solution.
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