IntegralBetween Command

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

Returns the definite integral of the difference f(x) ‐ g(x) in the interval [a, b].

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]

Returns the definite integral of the difference f(x) ‐ g(x) in the interval [a, b] and shadows the related area when Evaluate = true. In case Evaluate = false the related area is shaded but the integral value is not calculated.

CAS Syntax

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

Returns the definite integral of the difference f(x) ‐ g(x) in the interval [a, b].

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 ]

Returns the definite integral of the difference f ‐ g in the interval [a, b] with respect to the variable t.

Example:

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