calculus Calculators
Numerical Derivative Calculator
Compute the derivative of a polynomial term f(x) = c·xⁿ and evaluate it at a chosen x value using the power rule. Ideal for calculus students needing step-by-step differentiation of single-term expressions.
Rectangular Rule Integration
Approximates a definite integral over [a, b] by dividing the interval into equal rectangles and summing their areas. Ideal for numerical integration when an exact antiderivative is difficult or impossible to find.
Limit Calculator
Evaluate the limit of a rational function f(x) = (A·xᵐ) / (B·xⁿ) as x approaches a given value. Use this when analyzing function behavior, continuity, or derivatives from first principles.
Chain Rule Calculator
Computes the derivative of a composite function by multiplying the outer function's derivative by the inner function's derivative. Ideal for calculus students who have already evaluated each sub-derivative and need the final combined result.
Related Rates Calculator
Determines an unknown rate of change from a known rate using a proportional relationship between two quantities. Use it in calculus problems where two variables change together over time and one rate must be found from the other.
Critical Points Calculator
Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.
Trapezoidal Rule Calculator
Approximate the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.
Arc Length Calculator
Compute the approximate arc length of a curve f(x) between two x-values using a constant average derivative. Use this for a quick linear approximation when the exact integral is complex.
Optimization Calculator
Find the vertex (maximum or minimum) of a quadratic function f(x) = ax² + bx + c. Use this when solving real-world optimization problems like maximizing profit or minimizing cost.
Implicit Differentiation Calculator
Compute dy/dx for equations involving both x and y using implicit differentiation. Use this when y cannot be easily isolated as an explicit function of x.
Definite Integral Calculator
Numerically evaluates the definite integral of a power function ax^n over a specified interval. Choose from Simpson's Rule, Trapezoidal Rule, or the Midpoint Rectangle Method for your approximation.
Partial Derivative Calculator
Computes the partial derivative of a two-variable power function f(x,y) = aₓ·xᵐ·yⁿ with respect to either x or y at a specific point. Useful for multivariable calculus, gradient calculations, and optimization problems.
Taylor Series Calculator
Approximates the value of common functions (eˣ, sin x, cos x, ln x) using their Taylor series expansion around a chosen center point. Ideal for understanding polynomial approximations and truncation error in numerical analysis.
Implicit Differentiation Calculator
Finds the slope dy/dx of a conic section curve (circle or ellipse) defined by Ax² + By² = C at a specified point. Use it when the relationship between x and y cannot be solved explicitly for y.
Surface Area of Revolution Calculator
Calculates the surface area generated when the curve y = ax^n is revolved around the x-axis or y-axis between two bounds. Essential for 3D geometry, engineering design, and calculus coursework on solids of revolution.
Area Between Curves Calculator
Finds the enclosed area between two power-function curves over a chosen interval. Useful in calculus courses when computing regions bounded by f(x) = ax^n and g(x) = bx^m.
Average Value of Function Calculator
Computes the average value of f(x) = c·xⁿ + k over an interval [a, b]. Ideal for calculus students verifying the Mean Value Theorem for Integrals.
Tangent Line Calculator
Finds the equation of the tangent line to f(x) = c·xⁿ + k at a specified x-value. Use it to linearize a curve at any point for calculus or physics problems.
Concavity Calculator
Evaluates the second derivative of a cubic f(x) = ax³ + bx² + cx at a test point to determine concavity. Use it to classify intervals as concave up or concave down and locate inflection points.
Definite Integral Calculator
Compute the exact or approximate area under a polynomial curve between two bounds. Ideal for calculus students and engineers evaluating net change, area, or accumulated quantities.
First-Order ODE Solver
Solves first-order linear ODEs of the form a·y' + b·y = c with an initial condition y(0). Use it for physics, engineering, or math coursework whenever you need y(x) instantly.
Surface of Revolution Calculator
Calculates the surface area formed when a polynomial curve is rotated around the x-axis or y-axis over a chosen interval. Ideal for calculus courses and 3D design problems involving solids of revolution.
Area Under Curve Calculator
Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂]. Use it to evaluate definite integrals for quadratic functions in physics, economics, or calculus coursework.
Riemann Sum Calculator
Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums. Use this to understand numerical integration and error in calculus courses.
Definite Integral Calculator
Computes the exact area under the curve y = axⁿ + c between two x-values using the Fundamental Theorem of Calculus. Perfect for students solving area, displacement, or accumulation problems.
Chain Rule Derivative Calculator
Evaluates the derivative of a composite polynomial function y = a(bx + c)ⁿ at a given x value using the chain rule. Ideal for calculus learners verifying step-by-step differentiation of power-of-linear expressions.
Riemann Sum Calculator
Approximate the area under a curve f(x) = c·xⁿ using left, right, or midpoint rectangle sums. Ideal for calculus students learning numerical integration or checking definite integral estimates.
Critical Points Calculator
Find and classify critical points of a cubic polynomial ax³ + bx² + cx + d. Use it when you need to locate local maxima, minima, and inflection points quickly.
Related Rates Calculator
Calculate how fast the area or volume of a circle, sphere, or cylinder changes given the rate at which its radius is changing. Useful for calculus related-rates problems in physics and engineering.
Taylor Series Calculator
Approximate eˣ or sin(x) at any point using a Taylor series expansion centered at a chosen value. Perfect for understanding polynomial approximations in numerical analysis and calculus courses.