If for a continuous function f,
∫−aa f(x)dx=K∫0a (f(x)+f(−x))dx then the value of K is
1
1/2
2
a
∫−aa f(x)dx=∫−a0 f(x)dx+∫0a f(x)dx=−∫a0 f(−x)dx+∫0a f(x)dx=∫0a (f(−x)+f(x))dx.