Integration Tool

This applet allows you to integrate a function over a specified range. It uses a midpoint Riemann sum approximation in order to perform the integration numerically. To use it, simply input the function at the top, then set the starting and ending points, the number of steps or the size of each step and then click "Integrate!" at the bottom. See the syntax section below the applet to find out what kind of expressions you can use in the function field.

The applet allows you to enter functions with the following syntax:

• Number: '1', '0.1', '.1'
• Variable: 'x', 'X'; can be used wherever numbers can be used
• Addition: '1+2'
• Subtraction: '1-2'
• Multiplication: '1*2', '2*x', '2x', '2(x)'
• Division: '1/2'
• Exponents: '2^4'
• Unary Negation: '-1', '2--1' is the same as '2-(-1)'
• Parentheses: '1-(2+3)'
• Functions:
  • Sine: 'sin(0)'
  • Cosine: 'cos(0)'
  • Tangent: 'tan(0)'
  • Natural Logarithm: 'log(1)'
  • Absolute Value: 'abs(-30)'
  • Exponential: 'exp(2)'
  • Square Root: 'sqrt(4)'
  • Arc-tangent: 'atan2(4,2)'

For those who are interested, here is the grammar for mathematical expressions in this applet:

• EXPR ::= TERM { '+' TERM | '-' TERM }*
• TERM ::= UNARYNEG { '*' UNARYNEG | '/' UNARYNEG | UNARYNEG¹ }*
• UNARYNEG ::= ['-'] POWER
• POWER ::= FIELD ['^' UNARYNEG]
• FIELD ::= <num> | <var> | '(' EXPR ')' | <func> '(' EXPR [',' EXPR] ')'

¹ This option is only available if the UNARYNEG expression starts with a left parenthesis or is a variable. It's kind of a kludge, but it gets the right behavior, which allows for things like "2x".