8 / | | sin(x) | -------------- dx | ___________ | 3 / | 2 | | \/ |x - 16| | / 0
Integral(sin(x)/|x^2 - 16|^(1/3), (x, 0, 8))
/ / | | | sin(x) | sin(x) | -------------- dx = C + | -------------- dx | ___________ | ___________ | 3 / | 2 | | 3 / | 2 | | \/ |x - 16| | \/ |x - 16| | | / /
8 / | | / sin(x) 2 | |-------------------- for -16 + x >= 0 | |3 ________ 3 _______ | |\/ -4 + x *\/ 4 + x | < dx | | sin(x) | |------------------- otherwise | |3 _______ 3 _______ | \\/ 4 + x *\/ 4 - x | / 0
=
8 / | | / sin(x) 2 | |-------------------- for -16 + x >= 0 | |3 ________ 3 _______ | |\/ -4 + x *\/ 4 + x | < dx | | sin(x) | |------------------- otherwise | |3 _______ 3 _______ | \\/ 4 + x *\/ 4 - x | / 0
Integral(Piecewise((sin(x)/((-4 + x)^(1/3)*(4 + x)^(1/3)), -16 + x^2 >= 0), (sin(x)/((4 + x)^(1/3)*(4 - x)^(1/3)), True)), (x, 0, 8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.