Integral Calculator

Calculate definite integrals using numerical integration methods.

Function Type:

Coefficient (a):

Power (n):

Coefficient (b):

Constant (c):

Limits of Integration

Lower bound (a):

Upper bound (b):

Definite Integral

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Enter function and bounds

Antiderivative

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Area Under Curve

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Integration Rules

Integration is the reverse of differentiation. The definite integral represents the area under a curve between two points.

Basic Integration Rules

Power Rule: ∫x^n dx = x^(n+1)/(n+1) + C (n ≠ -1)
Constant: ∫c dx = cx + C
Sum: ∫(f+g) dx = ∫f dx + ∫g dx

Integrals of Common Functions

Function	Integral
sin(x)	-cos(x) + C
cos(x)	sin(x) + C
e^x	e^x + C
1/x	ln\|x\| + C
a^x	a^x / ln(a) + C
sec²(x)	tan(x) + C

Fundamental Theorem of Calculus

∫[a to b] f(x)dx = F(b) - F(a)

Where F(x) is the antiderivative of f(x).

Frequently Asked Questions

What is the difference between definite and indefinite integrals?

An indefinite integral finds the general antiderivative (with +C). A definite integral calculates the exact area between two bounds, giving a numerical result.

What does the integral represent physically?

The definite integral represents the accumulated quantity: area under a curve, total distance from velocity, total work from force, etc.