Definite integral
Calculation of `\int_a^b f(x) \ dx\text{ or }\int_-oo^b f(x) \ dx\text{ or }\int_a^{+oo} f(x)`
This tool is an online calculator of the integral of a function over an interval also called definite integral.
Usual functions are accepted: sine, cosine, tangent, logarithm (log), exponential, root, etc. (See table below).
You can enter lower and upper limits (boundaries of the integration interval) as values (1/2 for example), or constant (pi, e, etc.) or infinity (enter +inf or -inf for +/- infinity).
How to use this calculator ?
Variables | A function can have one or more variables, but only one main variable. A variable is a single lowercase or uppercase letter. Examples: A function f with one main variable : f(x) = 4*x A function g with one main variable x and a secondary parameter m, g(x) = 4*x*m + x + 1, In this case, enter x in the “main variable” field |
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Numbers | Use a dot as decimal separator |
Operators |
+ (addition), - (substration), * (multiplication), / (division), ^ (power), For multiply operator, enter a*b not a.b nor ab. Example: 2*x. |
Constants | You may use these constants : pi (approx. 3.14), e (approx. 2,72) Examples: f(x) = pi * x or f(x) = e * (x+1+2*e)^{2} |
Common Functions |
You may use theses functions in the expression of f(x) sqrt(x) (square root), exp(x) (exponential function), log(x) or ln (natural logarithm), |
Trigonometric functions |
You may use theses functions in the expression of f(x) sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), csc (cosecant), |
Inverse trigonometric functions |
You may use theses functions in the expression of f(x) arcsin (arcsine), arccos (arccosine), arctan (arctangent), arccot (arcotangent), arcsec (arcsecant), arccsc (arccosecant), |
Hyperbolic Functions |
You may use theses functions in the expression of f(x) sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), coth (hyperbolic cotangent), sech (hyperbolic secante), csch (hyperbolic cosecant) |
Inverse hyperbolic functions |
You may use theses functions in the expression of f(x) asinh (inverse hyperbolic sine), acosh (inverse hyperbolic cosine), atanh (inverse hyperbolic tangent), acoth (inverse hyperbolic cotangent), asech (inverse hyperbolic secant), acsch (inverse hyperbolic cosecant) |
See also
Derivative of a function
Primitive calculator
Taylor series expansion
Function limit
Value of a function