Calculator Inputs
Exact symbolic routines are optimized for single-variable polynomial expressions like 3*x^4 - 2*x^2 + 5*x - 7. Numeric evaluation and graphing also accept common functions such as sin, cos, sqrt, and log.
Example Data Table
Example expression: x^3 - 2*x + 1
| x | f(x) | Derivative | Integral |
|---|---|---|---|
| -2 | -3 | 3*x^2 - 2 | x^4/4 - x^2 + x + C |
| -1 | 2 | 3*x^2 - 2 | x^4/4 - x^2 + x + C |
| 0 | 1 | 3*x^2 - 2 | x^4/4 - x^2 + x + C |
| 1 | 0 | 3*x^2 - 2 | x^4/4 - x^2 + x + C |
| 2 | 5 | 3*x^2 - 2 | x^4/4 - x^2 + x + C |
Formula Used
1. Polynomial Simplification
Like terms are combined by summing coefficients that share the same exponent on the chosen variable.
2. Derivative Rule
d/dx (a*xn) = a*n*xn-1
3. Integral Rule
∫ a*xn dx = a/(n+1) * xn+1 + C, for n ≠ -1.
4. Numeric Evaluation
The selected variable is replaced with a numeric value, then the expression is computed using standard arithmetic and supported functions.
5. Graph Generation
The graph samples many x-values over the chosen range and plots the corresponding y-values to show expression behavior visually.
How to Use This Calculator
Enter a symbolic expression using one main variable, such as x^4 - 3*x + 2.
Set the variable name, choose the evaluation value, and define the graph range and step.
Press Calculate Symbolic Results to generate simplification, derivative, integral, numeric output, table, and graph.
Use polynomial formatting for exact symbolic results. Use functions for numeric evaluation and plotting where needed.
Download the generated table and summary with the CSV and PDF export buttons shown in the results section.
FAQs
1. What expressions work best for exact symbolic output?
Single-variable polynomials work best, such as 4*x^3 - 7*x + 2. These formats allow simplification, differentiation, and integration to be shown exactly.
2. Can the calculator evaluate expressions with functions?
Yes. Numeric evaluation and graphing can handle common functions like sin, cos, sqrt, log, and exp, provided the syntax is standard.
3. Why is there a constant C in the integral?
Indefinite integration represents a family of antiderivatives. The constant C accounts for every possible vertical shift of the integrated function.
4. Why might symbolic results be unavailable?
Exact symbolic routines are limited to polynomial-style inputs. Expressions with unsupported structures may still evaluate numerically and graph correctly.
5. What does the graph actually show?
The graph shows sampled numeric points from your selected range. It helps you inspect growth, turning behavior, sign changes, and approximate shape.
6. How many rows can the generated table include?
The generated table is capped to keep the page practical and readable. Use a larger step size when you want a broader range quickly.
7. Can I change the variable from x to another letter?
Yes. Enter one lowercase letter as the primary variable. Keep the same letter throughout the expression for consistent symbolic handling.
8. What do the CSV and PDF exports include?
They include the expression details, summary outputs, and generated value table. This makes sharing, documentation, and offline review much easier.