- Topic
- Antiderivatives
- Difficulty
- Standard
- Suggested time
- 4 min
- Marks
- 2
- Theory
- CLP-1 §4.1Key results
Antiderivatives practice question 11
A function satisfies the conditions below. A student finds as shown. Find the first line that is wrong.
Each line can be checked on its own: differentiate an antiderivative to see whether it gives back , and redo each substitution.
Differentiate line 1 and see whether you get back .
When you raise the power by one, which exponent do you divide by: the old one, or the new one?
Theory CLP-1 §4.1Key results
Corrected working
Strategy
Antidifferentiate term by term, fix the constant from F(1) = 3, then evaluate.
Working
Raise each power by one and divide by the new exponent.
The condition fixes C.
Substitute x = 2.
Answer
The answer is F of 2 equals 21.
Check
x⁴ + x² + 1 differentiates back to 4x³ + 2x and is 3 at x = 1, while 4x⁴/3 + 2x² differentiates to 16x³/3 + 4x.
Where this goes wrong
Dividing by the old exponent. After raising the power by one, divide by the new exponent; differentiating the result is the quick check.
Leans on
The power rule, from Differentiation rules
Try a similar question
A function satisfies and . Find .Saved in this browser only.