The names {{CMD_222}}odd{{CMD_223}} and {{CMD_224}}even{{CMD_225}} come from the fact that these properties are shared by functions of the form {{MATH_226}} where {{MATH_227}} is either odd or even. For example, if {{MATH_228}}, then {{MATH_229}} and if {{MATH_230}}, then {{MATH_231}} Geometrically, even functions have symmetry with respect to the {{MATH_232}}axis . Cosine is an even function: {{CMD_233}} {{ENV_234}} {{CMD_235}} On the other hand, odd functions have {{MATH_236}} {{CMD_237}}rotational symmetry{{CMD_238}} around the origin. Sine is an odd function: {{CMD_239}} {{ENV_240}} {{CMD_241}} {{CMD_242}} Let {{MATH_243}} be an odd function defined for all real numbers. Compute: {{MATH_244}} {{CMD_245}} Since our function is odd, it must look something like: {{CMD_246}} {{ENV_247}} {{CMD_248}} {{CMD_249}} {{CMD_250}} The integral above computes the following net area: {{CMD_251}} {{ENV_252}} {{CMD_253}} {{CMD_254}} {{CMD_255}}