Question

State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_(-"b")^(-"a") f(x)*dx`

Options

• True

• False

Answer 1

Let I = `int_"a"^"b" f(x)*dx`
Put x = – 1
∴ dx = – dt
When x = a, t = – a
When x = b, t = – b

∴ I = `int_(-a)^(-b) f(-"t") (-"dt")`

= `int_(-"b")^(-"a") f(- "t")*"dt"      ...[because int_"a"^"b" f(x)*dx = -int_"b"^"a" f(x)*dx]`

= `int_(-"b")^(-"a") f(-x)*dx       ...[because int_"a"^"b" f(x)*dx = int_"a"^"b" f("t")*dt]`.