JEE Main202312 Apr 2023Morning ShiftMathematicsDefinite IntegrationActual
If ∫ - 0 . 15 0 . 15 100 x 2 - 1 d x = k 3000 , then k is equal to _____.
Correct answer
0
Step-by-step solution
Given, ∫ - 0 . 15 0 . 15 100 x 2 - 1 d x = k 3000 Now we know that, ∫ - a a f x d x = 2 ∫ 0 a f x d x   if   f x   is even So, ∫ - 0 . 15 0 . 15 100 x 2 - 1 d x = 2 ∫ 0 0 . 15 100 x 2 - 1 d x Now solving, 2 ∫ 0 0 . 15 100 x 2 - 1 d x = 2 ∫ 0 0 . 1 - 100 x 2 - 1 d x + ∫ 0 . 1 0 . 15 100 x 2 - 1 d x ⇒ 2 ∫ 0 0 . 15 100 x 2 - 1 d x = 2 x - 100 x 3 3 0 0 . 1 + 100 x 3 3 - x 0 . 1 0 . 15 ⇒ 2 ∫ 0 0 . 15 100 x 2 - 1 d x = 2 1 10 - 1