Calculus Tools
Derivatives, integrals, limits, Taylor series, area under curves, arc length, solids of revolution, partial derivatives, gradients, and Laplace transforms.
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Arc Length Calculator
Calculate the arc length of linear, quadratic, and circular curves between two points using numerical integration.
Area Under Curve Calculator
Approximate the area under f(x) = x² using trapezoidal, Simpson's, or midpoint rule. Compare with the exact answer.
Derivative Calculator
Calculate the derivative of polynomial, trigonometric, exponential, and logarithmic functions at any point.
Gradient Vector Calculator
Calculate the gradient vector of f(x,y) = ax² + by² + cxy at any point. Shows magnitude and direction of steepest ascent.
Integral Calculator
Calculate definite integrals of polynomial, trigonometric, and exponential functions over any interval.
Laplace Transform Calculator
Compute Laplace transforms of common functions: exponential, sine, cosine, polynomial, and Heaviside step.
Limit Calculator
Evaluate limits of rational, trigonometric, and exponential functions. Shows left limit, right limit, and existence.
Partial Derivative Calculator
Calculate partial derivatives of f(x,y) = axy + bx² + cy² + d. Find df/dx, df/dy, and the gradient magnitude.
Taylor Series Calculator
Approximate functions using Taylor series expansion. Compare the approximation with the exact value for sin, cos, e^x, and ln(x).
Volume of Revolution Calculator
Calculate the volume and surface area of a solid of revolution using the disk or shell method.