Practice Flashcards
Flip to reveal answersWhat is integration?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 9 Flashcards — Antidifferentiation
Sign up free to track progress and get spaced-repetition review schedules.
Question
What is integration?
Answer
The reverse of differentiation (antidifferentiation).
Question
State the rule for ∫xⁿ dx.
Answer
xⁿ⁺¹/(n+1) + C, for n ≠ −1.
Question
Why must you add + C to an indefinite integral?
Answer
Differentiating any constant gives 0, so the original could have had any constant.
Question
How do you integrate a constant like 5?
Answer
It becomes 5x (5 = 5x⁰, add 1 to the power).
Question
How do you integrate a polynomial?
Answer
Integrate each term with the power rule, then add a single + C.
Question
∫√x dx = ?
Answer
∫x^(1/2) dx = (2/3)x^(3/2) + C.
Question
∫1/x² dx = ?
Answer
∫x⁻² dx = −1/x + C.
Question
How do you find f(x) from f'(x) and a point?
Answer
Integrate f'(x) (with + C), then substitute the point to find C.
Question
Which power can't you integrate with this rule?
Answer
n = −1 (∫x⁻¹ dx = ln|x| + C, a special case).
Read the notes
Full study notes for Antidifferentiation
Topic 5.5 hub
Introduction to integration
More from Topic 5.5
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free