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