IntegralBetween Command

IntegralBetween[ >Function f>, <Function g>, <Number a>, <Number b> ]

Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the main variable.

Note: This command also shades the area between the function graphs of f and g.

IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b>, <Boolean Evaluate> ]

Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the main variable and shadows the related area if Evaluate is true. In case Evaluate is false the related area is shaded but the integral value is not calculated.

CAS Syntax

IntegralBetween[ <Function f>, <Function g>, <Number a>, <Number b> ]

Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the main variable.

Example:

IntegralBetween[sin(x), cos(x), π / 4, π * 5 / 4] yields 2 \sqrt{2}.

IntegralBetween[ <Function f>, <Function g>, <Variable t>, <Number a>, <Number b> ]

Gives the definite integral of the difference f(x) ‐ g(x) over the interval [a, b] with respect to the given variable.

Example:

IntegralBetween[a * sin(t), a * cos(t), t, π / 4, π * 5 / 4] yields 2 \sqrt{2} a.