Select a function to differentiate symbolically, or evaluate at a point.
xnsin(x)cos(x)tan(x)exln(x)√xax²+bx+c
Select a function for indefinite integration, or enter bounds for definite integral.
xnsin(x)cos(x)sec²(x)ex1/x√xax²+bx+c
Quick Answer – What is Calculus?
Calculus is the mathematical study of continuous change. It has two main branches: differential calculus (rates of change and slopes of curves, via derivatives) and integral calculus (accumulation of quantities and areas under curves, via integrals). Limits form the foundational concept defining both derivatives and integrals.
Key Rules & Formulas
Limit: limx→a f(x)
Power Rule: d/dx [xn] = n xn−1
d/dx[sin x] = cos x, d/dx[cos x] = −sin x
∫ xn dx = xn+1/(n+1) + C (n ≠ −1)
∫ sin x dx = −cos x + C, ∫ cos x dx = sin x + C
Definite: ∫ab f(x) dx = F(b) − F(a)
Solved Examples
Example 1: Limit limx→2 x²
Direct substitution: 2² = 4
Example 2: Derivative of x³ at x=2
d/dx[x³] = 3x²; at x=2: 3×4 = 12
Example 3: ∫01 x² dx
Antiderivative: x³/3 | from 0 to 1 = (1/3) − (0) = 1/3 ≈ 0.3333
Frequently Asked Questions
Q1. How do I enter limits at infinity?
Type inf for +∞ and -inf for −∞. The calculator evaluates the asymptotic behaviour of the selected function.
Q2. Can I get a symbolic derivative?
Yes, the derivative tab shows the general derivative formula (e.g., d/dx[x³] = 3x²). You can optionally evaluate it at a specific x.
Q3. What integration rules are supported?
Basic power rule, trigonometric (sin, cos, sec²), exponential, natural log, and simple polynomials. For more complex functions, use the polynomial option with coefficients.
Q4. How precise are the numerical evaluations?
Results are computed using standard JavaScript Math functions with double‑precision floating point, displayed to 6 decimal places.
Q5. Can I enter arbitrary coefficients for polynomials?
Yes, select the "ax²+bx+c" chip and enter your own a, b, c values. The calculator evaluates limits, derivatives, and integrals for your custom quadratic.