int_2^7f(x)dx=5 হলে int_0^1f(5x+2)dx এর মান হবে-

Explanation:

Another Explanation (5): bài toán: \(\int_2^7 f(x) dx = 5\) হলে, \(\int_0^1 f(5x+2) dx\) এর মান নির্ণয় করো। সমাধান: ধরি, \(u = 5x + 2\). তাহলে, \(\frac{du}{dx} = 5\) বা, \(dx = \frac{du}{5}\). যখন \(x = 0\), \(u = 5(0) + 2 = 2\). যখন \(x = 1\), \(u = 5(1) + 2 = 7\). সুতরাং, \(\int_0^1 f(5x+2) dx = \int_2^7 f(u) \frac{du}{5}\) \( = \frac{1}{5} \int_2^7 f(u) du\) যেহেতু \(\int_2^7 f(x) dx = 5\), \(\int_0^1 f(5x+2) dx = \frac{1}{5} \times 5 = 1\) অতএব, \(\int_0^1 f(5x+2) dx = 1\). 🥳