Integrate a polynomial coefficient list exactly and append the constant term. The result panel keeps antiderivative coefficients and its numerical trail together.
The reverse power rule raises each exponent by one and divides its coefficient by that new exponent.
The roles assigned to polynomial coefficients, highest power first explain the operation that produces antiderivative coefficients.
Exact polynomial antiderivatives support definite integrals and differential-equation checks. A related application of Polynomial Antiderivative is differentiate back.
The arbitrary constant represents every function sharing the same derivative; the coefficient list displays zero for one chosen constant.
A rough estimate made before calculating gives the finished antiderivative coefficients a useful plausibility check.
3x³−2x²+5 integrates to .75x⁴−(2/3)x³+5x+C.
Label powers, divide each coefficient by exponent plus one, and append zero before writing +C. Polynomial Antiderivative also leads to bounded integral.
Before entering polynomial coefficients, highest power first, identify what each field represents. Its label determines how the polynomial antiderivative relationship interprets the entry. The browser cannot supply missing unit context, so preserve that context in your notes.
Changing the integration constant shifts the antiderivative without changing its derivative. That behavior gives the polynomial antiderivative output a built-in reasonableness test.
A final answer should carry enough context to be reusable: name it antiderivative coefficients, attach any applicable unit, and record the rounding point. If another person must reproduce the result, the supplied input in the field and the displayed formula are more informative than the decimal alone.
The definite-integral page evaluates a numerical accumulation over bounds. Writing “Antiderivative coefficients” beside the output prevents that mix-up.
A useful note for this result contains the Polynomial Antiderivative entries (polynomial coefficients, highest power first), the answer label, and the chosen precision. That record can be checked without recreating the entire page state.
For Polynomial Antiderivative, retain Polynomial coefficients, highest power first. Compare the numerical output with a function whose exact calculus result is already known. A polynomial, constant, or simple exponential supplies a useful control before applying the same settings to a less familiar expression. Record which control was used.
For this polynomial antiderivative result, write down the expression exactly as entered, then note the evaluation point or interval. That small record makes it possible to repeat the computation and investigate any disagreement without guessing at the original setup.
Derivatives erase constants.
Yes for the coefficient model.
Differentiate the result.