Polynomial calculus
Evaluate the derivative and definite integral of ax² + bx + c.
How this works
For f(x)=ax²+bx+c, f′(x)=2ax+b and F(x)=ax³/3+bx²/2+cx. Integral = F(upper)−F(lower).
Example
Using the example inputs, derivative at x is 4.
- a coefficient
- 1
- b coefficient
- 0
- c coefficient
- 0
- Derivative at x
- 2
- Integral lower bound
- 0
- Integral upper bound
- 3
- Derivative at x
- 4
The integral is signed area; reversing bounds changes its sign.
Scope and assumptions
Polynomials through degree 2 only. No general integrals, limits, or symbolic expression input.
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