NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice
The value of ∫ 0 2 x 4 4 - x 2 d x ∫ 0 2 x 2 4 - x 2 d x is equal to
Correct answer
2
Step-by-step solution
∫ 0 2 x 4 4 - x 2 d x = - 1 2 ∫ 0 2 x 3 ⏟ Ι - 2 x 4 - x 2 ⏟ Ι Ι d x Using integration by parts, we get = - 1 2 x 3 4 - x 2 3 2 3 2 0 2 - ∫ 0 2 3 x 2 4 - x 2 3 2 3 2 d x = - 1 2 0 - 0 - ∫ 0 2 2 x 2 4 - x 2 3 2 d x = ∫ 0 2 x 2 4 - x 2 3 2 d x = ∫ 0 2 x 2 4 - x 2 4 - x 2 d x ⇒ ∫ 0 2 x 4 4 - x 2 d x = 4 ∫ 0 2 x 2 4 - x 2 d x - ∫ 0 2 x 4 4 - x 2 d x ⇒ 2 ∫ 0 2 x 4 4 - x 2 d x = 4 ∫ 0 2 x 2 4 - x 2 d x ⇒ ∫