The odd natural number a, such that the area of the region bounded by y = 1 , y = 3 , x = 0 , x = y a is 364 3 , equal to:

Step-by-step solution

Plotting the graph of the given functions, we get the shaded region as the area bounded by the curves. Given, area of shaded region = 364 3 ⇒ ∫ 1 3 y a d y = 364 3 ⇒ y a + 1 a + 1 1 3 = 364 3 ⇒ 3 a + 1 - 1 a + 1 = 364 3 = 729 - 1 6 = 3 6 - 1 6 ⇒ a = 5