Trong mỗi ý a), b), c), d) ở mỗi câu, thi sinh chọn đúng hoặc sai
Trong mặt phẳng tọa độ Oxy, xét parabol \(({\rm{P}}):{\rm{y}} = {{\rm{x}}^2} - 4.\)
Trong mặt phẳng tọa độ Oxy, xét parabol \(({\rm{P}}):{\rm{y}} = {{\rm{x}}^2} - 4.\)
a) Hoành độ giao điểm của \(({\rm{P}})\) và Ox là -2 và 2.
b) \(\int {\left( {{x^2} - 4} \right)} dx = \frac{{{x^3}}}{3} + 4x + C.\)
c) \(\left| {{x^2} - 4} \right| = {x^2} - 4\forall x \in [ - 2;2]\)
d) Diện tích hình phẳng giới hạn bởi \(({\rm{P}})\) và Ox bằng \(\frac{{32}}{3}.\)
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
- a) Parabol $(P)$ có phương trình $y = x^2 - 4$. Giao điểm của $(P)$ và trục Ox có tung độ bằng 0. Vậy ta có $x^2 - 4 = 0 \Leftrightarrow x = \pm 2$. Vậy hoành độ giao điểm là -2 và 2.
- b) Ta có $\int (x^2 - 4) dx = \frac{x^3}{3} - 4x + C$. Do đó, khẳng định này sai.
- c) Xét $x \in [-2; 2]$, ta có $x^2 \le 4 \Rightarrow x^2 - 4 \le 0 \Rightarrow |x^2 - 4| = -(x^2 - 4) = 4 - x^2 \neq x^2 - 4$. Vậy khẳng định này sai.
- d) Diện tích hình phẳng giới hạn bởi $(P)$ và Ox là $S = \int_{-2}^2 |x^2 - 4| dx = \int_{-2}^2 (4 - x^2) dx = (4x - \frac{x^3}{3})|_{-2}^2 = (8 - \frac{8}{3}) - (-8 + \frac{8}{3}) = 16 - \frac{16}{3} = \frac{32}{3}$. Vậy khẳng định này đúng.
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We are thrilled to announce that (1) ______ Nick Vujicic will be visiting our community for an exclusive seminar (2) ______ to inspire, empower, and create lasting change. This once-in-a-lifetime event will offer attendees the opportunity to hear Nick's powerful story of resilience, faith, and perseverance firsthand. Born without limbs, Nick has transformed his circumstances into a source of (3) ______. He has spoken to millions of people around the globe, spreading messages of hope, and the courage to turn obstacles (4) ______ opportunities. Nick’s dynamic and engaging approach has (5) ______ a lasting impact on audiences of all ages and backgrounds. Participants will gain practical strategies for overcoming challenges, achieving personal and professional goals. This event is organized (6) ______ personal growth, motivate change, and cultivate unity. Join us for an unforgettable experience. Space is limited, so be sure to reserve your spot today!
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Colors of Humanity: Experience the World in One Place
Join our amazing cultural festival!
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Location: City Park
Free entry for children
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