- Topic
- Antiderivatives
- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
- Theory
- CLP-1 §4.1Key results
Antiderivatives practice question 1
A function satisfies and . Find .
Knowing pins down only up to a constant. Which given fact fixes that constant?
Antidifferentiate term by term (each comes from ), add a constant , and use to find .
A whole number.
Theory CLP-1 §4.1Key results
Worked solution
Strategy
Reverse the power rule on each term, remember the constant of integration, and fix the constant from the given value.
Working
Check by differentiating: 6x² − 4x + 1.
Initial condition.
Evaluate.
Answer
The answer is 3.
Check
Differentiating 2x³ − 2x² + x + 2 gives back 6x² − 4x + 1, and its value at x = 0 is 2, as required.
Where this goes wrong
Forgetting the constant and answering F(1) = 1. The derivative determines F only up to a constant; the condition F(0) = 2 is there to pin it down.
Leans on
The power rule, from Differentiation rules
Try a similar question
A function satisfies , and . Find .Saved in this browser only.