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KCET2018MathematicsDefinite Integration

( _ -2 ²|x x| d x ) is equal to

Options

  1. A( 8 )
  2. B( 4 )
  3. C( 2 )
  4. D( 1 )

Correct answer

A. ( 8 )

Step-by-step solution

Given that, [ array l _ -2 ²|x x| d x=2 ₀²|x x| d x =2 [ ₀^ 1 / 2 x x- _ 1 / 2 ^ 3 / 2 (x x) d x+ _ 3 / 2 ²(x x) d x ] =2 [ 1 2 - 1 ² + 4 2 + 3 2 + 1 ² ] =2 ( 8 2 )= 8 array ]

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₀^1 2 x+5 x^2+3 x+2 ~d x= 2025₀^1 x^ 5 / 2 (1-x)^ 3 / 2 ~d x= 2025_ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + 3 n^2 ^2 9 n^2 + + 1 n^2 ^2 1 ]= 2025₀^1 x Sin ⁻¹ x d x= 2025_ - 2 ^ 2 (x-[x]) d x= 2025₀^2 x^2(2-x)^5 d x= 2025If f(x)= Max x^3-4, x^4-4 , and g(x)= Min x^2, x^3 , then _ -1 ^1(f(x)-g(x)) d x= 2025_ n 2 n [ 2 n + 2 2 n + 3 2 n + + 2 ]= 2025 Full Definite Integration list All KCET PYQs