The value of ∫ 0 1 4 x 3 d 2 d x 2 1 - x 2 5 d x is ____________

Step-by-step solution

∫ 0 1 4 x 3 ⏟ d 2 d x 2   1 - x 2 5 ⏟ d x = 4 x 3 d d x   1 - x 2 5 0 1 -   ∫ 0 1 12 x 2 d d x   1 - x 2 5   d x = 4 x 3   × 5 1 - x 2 4   - 2 x 0 1 - 12 x 2 1 - x 2 5 0 1 -   ∫ 0 1 2 x 1 - x 2 5 d x = 0 - 0 - 12 0 - 0 + 12   ∫ 0 1 2 x 1 - x 2 5   d x = 12   × - 1 - x 2 6 6 0 1 = 12 0 + 1 6 = 2