Explanation: 
Another Explanation (5):
ধরি, \(I = \int_1^4 f(5-x) \, dx\)
এখানে, \(5-x = t\) ধরলে, \(-dx = dt\) হয়। সুতরাং, \(dx = -dt\).
যখন \(x = 1\), তখন \(t = 5-1 = 4\) এবং যখন \(x = 4\), তখন \(t = 5-4 = 1\).
অতএব,
\(I = \int_4^1 f(t) (-dt)\)
\(I = - \int_4^1 f(t) \, dt\)
আমরা জানি, \(\int_a^b f(x) \, dx = - \int_b^a f(x) \, dx\). সুতরাং,
\(I = \int_1^4 f(t) \, dt\)
যেহেতু \(\int_a^b f(x) \, dx = \int_a^b f(t) \, dt\), তাই
\(I = \int_1^4 f(x) \, dx\)
প্রশ্নানুসারে, \(\int_1^4 f(x) \, dx = 6\).
সুতরাং, \(I = 6\).
অতএব, \(\int_1^4 f(5-x) \, dx = 6\) 🥳
