Let `f(x)` be a continuous and periodic function such that `f(x)=f(x+T)` for all `xepsilonR,Tgt0`.If `int_(-2T)^(a+5T)f(x)dx=19(ag0)` and `int_(0)^(T)

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Let `f(x)` be a continuous and periodic function such that `f(x)=f(x+T)` for all `xepsilonR,Tgt0`.If `int_(-2T)^(a+5T)f(x)dx=19(ag0)` and `int_(0)^(T)

Let `f(x)` be a continuous and periodic function such that `f(x)=f(x+T)` for all `xepsilonR,Tgt0`.If `int_(-2T)^(a+5T)f(x)dx=19(ag0)` and `int_(0)^(T)f(x)dx=2`, then find the value of `int_(0)^(a)f(x)dx`.

Monjur Alahi

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2025-01-04 04:42

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Given that
`int_(-2T)^(a+5T)f(x)dx=19`
`=int_(-2T)^(5T)f(x)dx+int_(5T)^(5T)f(x)dx=19`
`implies7 int_(0)^(T)f(x)dx+int_(0)^(a)f(x)dx=19`
`implies int_(0)^(a)f(x)dx=19-7xx19-14=5`

5 views Answered 2023-02-05 15:29