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How to Use the Calculus Solver
Explicit functions (f(x)):
- Type a function in terms of x only. Example:
x^3, sin(3*x), arcsin(x).
- Click Derivative to see the first derivative, or Next Derivative for higher-order derivatives.
- Only the x value is needed for evaluation.
Implicit functions (F(x,y) = 0):
- Type an equation using "=", e.g.,
x^2 + y^2 = 25.
- Click Implicit dy/dx to compute the derivative implicitly.
- For evaluation, both x and y values are needed.
Integrals:
- Type a function and click Integral for the indefinite integral (antiderivative + C).
- Click Definite ∫ to show bound inputs, enter lower and upper bounds, then click Compute.
- Powered by Algebrite CAS, Nerdamer CAS, and a custom rule engine — handles polynomials, rational functions, trig, exponentials, logarithms, products like x*sin(x), compositions, and much more.
- Applies integration by parts, u-substitution, trig identities, and power reduction formulas.
- For non-elementary integrals (e.g., sin(sin(cos(x)))), produces Taylor series polynomial approximations integrated term by term.
- Results are verified by differentiation. Final fallback: adaptive Simpson's rule with near-exact numerical precision.
Area Between Curves:
- Enter 2 or more functions in the Area Between Curves section.
- Click Compute Area to find the area of the region bounded between the curves.
- Intersection points are found automatically. Optionally specify bounds to restrict the region.
- Computes ∫|f(x) − g(x)| dx over each sub-interval between intersection points.
- Click + Add Curve to add more functions. Click × to remove one (minimum 2).
Euler's Method:
- Click Euler's Method to open the panel.
- Enter dy/dx = f(x, y), initial values x₀ and y₀, step size h, and target x.
- Click Compute to see a step-by-step table of approximations.
- The graph plots the Euler approximation curve alongside the slope field.
- Useful for AP Calculus BC: numerically approximate solutions to differential equations.
Using Math Symbols:
- Click any symbol button to insert it into the function input
- Use the "arc" button followed by a trig function for inverse trig functions
- Constants like π and e are automatically recognized