If _ x 0 (e^ k x -1 ) k x x² =4 , then k is equal to

Step-by-step solution

aligned & _ x 0 (e^ k x -1 ) k x x² =4 & _ x 0 [ e^ k x k x x² - k x x² ]=4 & _ x 0 [ e^ k x k x k+k e^ k x k x 2 x - k k x 2 x ]=4 & _ x 0 [ k² e^ k x k x-k² e^ k x k x+k² e^ k x k x +k² e^ k x k x 2 . & k²-0+0+k² 2 +0=4 & k²=4 & k= 2 aligned