Definite Integral Calculator
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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)
More References and Links integrals
University 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