Definite Integral Calculator
\( \)\( \)\( \)\( \)A calculator for definite integrals is presented.
Definition of Definite Integral
The indefinite integral \( \displaystyle \int f(x) dx \) of function \( f(x) \) is given by
\[ \displaystyle \int f(x) dx = F(x) + C \]
such that \( F'(x) = f(x) \).
\( C \) is the constant of integration and \( F(x) \) is called the antiderivative.
The definite integral is defined by: \[ \displaystyle \int_a^b f(x) dx = F(b) - F(a) \]
Use of the Definite Integral Calculator
1 - Enter and edit function $f(x)$ and click "Enter Function" then check what you have entered and edit if needed.
Note that the five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x^3 - 2*x + 3*cos(3x-3) + e^(-4*x)).(more notes on editing functions are located below)
2 - Click "Calculate Integral" to obain the antiderivative \( \displaystyle F(x) \).
Notes: In editing functions, use the following:
1 - The inverse trigonometric functions are entered as: arcsin() arccos() arctan() and the inverse hyperbolic functions are entered as: arcsinh() arccosh() arctanh()
1 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = 2*x^3 + 3*cos(2x - 5) + ln(x))
2 - The function square root function is written as (sqrt). (example: sqrt(x^2-1)
3 - The exponential function is written as (e^x). (Example: e^(2*x+2) )
4 - The log base e function is written as ln(x). (Example: ln(2*x-2) )
Here are some examples of functions that you may copy and paste to practice:
x^2 + 2x - 3 (x^2+2x-1)/(x-1) 1/(x-2) ln(2*x - 2) sqrt(x^2-1)
2*sin(2x-2) e^(2x-3)
1/sqrt(x^2-1) 1/sqrt(1-x^2)
More References and Links
integralsUniversity Calculus - Early Transcendental - Joel Hass, Maurice D. Weir, George B. Thomas, Jr., Christopher Heil - ISBN-13 ? : ? 978-0134995540
Calculus - Gilbert Strang - MIT - ISBN-13 ? : ? 978-0961408824
Calculus - Early Transcendental - James Stewart - ISBN-13: 978-0-495-01166-8