Integral Calculator
Calculate indefinite and definite integrals with step-by-step solutions
Integration Rules
Basic Rules
Power Rule: ∫x^n dx = x^(n+1)/(n+1) + C
Constant Rule: ∫c dx = cx + C
Sum Rule: ∫(f + g) dx = ∫f dx + ∫g dx
Exponential: ∫e^x dx = e^x + C
Logarithmic: ∫1/x dx = ln|x| + C
Trigonometric
∫sin(x) dx = -cos(x) + C
∫cos(x) dx = sin(x) + C
∫tan(x) dx = -ln|cos(x)| + C
∫sec(x) dx = ln|sec(x) + tan(x)| + C
∫sec²(x) dx = tan(x) + C
Applications
Physics
- Area under curves
- Work and energy calculations
- Center of mass
- Moment of inertia
Engineering
- Signal processing
- Control systems
- Structural analysis
- Fluid dynamics
What is an Integral?
An integral represents the accumulation of quantities and can be interpreted as the area under a curve. Indefinite integrals give the antiderivative (reverse of differentiation), while definite integrals calculate the exact area between two points on the x-axis.