Practice question · Put in order
Order the steps for finding the one antiderivative of f that passes through a given point.
- Solve the resulting equation for C
- Integrate f term by term using the power rule and the standard forms
- Write out the particular antiderivative with C replaced by its value
- Write the general antiderivative F(x) with its constant of integration C
- Substitute the given point's coordinates into F(x)
Hints
- The constant has to be present before a condition can pin it down.
- You cannot solve for C until the point has been substituted in.
Show the answer
- Integrate f term by term using the power rule and the standard forms
- Write the general antiderivative F(x) with its constant of integration C
- Substitute the given point's coordinates into F(x)
- Solve the resulting equation for C
- Write out the particular antiderivative with C replaced by its value
Why
Integration produces a family; the point selects one member. Attempting to substitute before writing + C leaves nothing to solve for, which is why the constant must be carried from the very first line.
Practise Antiderivatives and Indefinite Integrals
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