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Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

Paragraph: It is known that x + x = cases x x + x x & if 0 x 2 - x - x + - x - x & if x 3 2 cases Question: The value of integral 1= ( x + x ) dx , where x (0, 2 ) ( , 3 2 )

Options

  1. A2 ⁻¹ ( x - x 2 )+c
  2. B2 ⁻¹ ( x + x 2 )+c
  3. C- 2 ⁻¹ ( x - x 2 )+c
  4. D- 2 ⁻¹ ( x + x 2 )+c

Correct answer

A. 2 ⁻¹ ( x - x 2 )+c

Step-by-step solution

For interval x (0, 2 ) aligned & 1= ( x + x ) d x= ( x x + x x ) d x & = x+ x x x d x= 2 ( x+ x) 2 x d x & = 2 x+ x 1-( x- x)^2 d x= 2 ⁻¹( x- x)+c aligned Put x- x=1 aligned & I = 2 ⁻¹( x- x)+ c x (0, 2 ) & I = 2 ⁻¹ ( x- x 1-( x- x)^2 ) & I = 2 ⁻¹ ( x- x) 2 x x ) )+9 & I = 2 ⁻¹ ( x (- x x 2 )+ c aligned aligned & x (0, 2 ) for interval x ( , 3 2 ) & I= ( x + x ) d x=- x+ x x x d x & I=- 2 ⁻¹( x- x)+c & I= 2 ⁻¹( x- x)+c x ( , 3 2 ) & I= 2 ⁻¹ ( x- x 1-( x- x)^2 )+c & I= 2 ⁻¹ ( x- x 2 x x )+c & I= 2 ⁻¹ ( x - x 2 )+c x

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