1 / | | sin(a*x)*cos(b*x) dx | / 0
// 0 for And(a = 0, b = 0)\ || | || 2 | || cos (b*x) | || --------- for a = -b | || 2*b | / || | | || 2 | | sin(a*x)*cos(b*x) dx = C + |< -cos (b*x) | | || ----------- for a = b | / || 2*b | || | || a*cos(a*x)*cos(b*x) b*sin(a*x)*sin(b*x) | ||- ------------------- - ------------------- otherwise | || 2 2 2 2 | || a - b a - b | \\ /
/ 0 for Or(And(a = 0, b = 0), And(a = 0, a = b, b = 0), And(a = 0, a = -b, b = 0), And(a = 0, a = -b, a = b, b = 0)) | | 2 | 1 cos (b) | - --- + ------- for Or(And(a = 0, a = -b), And(a = -b, a = b), And(a = -b, b = 0), And(a = 0, a = -b, a = b), And(a = -b, a = b, b = 0), a = -b) | 2*b 2*b | | 2 < 1 cos (b) | --- - ------- for Or(And(a = 0, a = b), And(a = b, b = 0), a = b) | 2*b 2*b | | a a*cos(a)*cos(b) b*sin(a)*sin(b) |------- - --------------- - --------------- otherwise | 2 2 2 2 2 2 |a - b a - b a - b \
=
/ 0 for Or(And(a = 0, b = 0), And(a = 0, a = b, b = 0), And(a = 0, a = -b, b = 0), And(a = 0, a = -b, a = b, b = 0)) | | 2 | 1 cos (b) | - --- + ------- for Or(And(a = 0, a = -b), And(a = -b, a = b), And(a = -b, b = 0), And(a = 0, a = -b, a = b), And(a = -b, a = b, b = 0), a = -b) | 2*b 2*b | | 2 < 1 cos (b) | --- - ------- for Or(And(a = 0, a = b), And(a = b, b = 0), a = b) | 2*b 2*b | | a a*cos(a)*cos(b) b*sin(a)*sin(b) |------- - --------------- - --------------- otherwise | 2 2 2 2 2 2 |a - b a - b a - b \
Use the examples entering the upper and lower limits of integration.