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NDA2022MathematicsDefinite IntegrationActual

What is ₀^ 4 d x ( x+ x)^2 equal to?

Options

  1. A- 1 2
  2. B1 2
  3. C1
  4. D3 2

Correct answer

B. 1 2

Step-by-step solution

aligned & ₀^ 4 d x ( x+ x)^2 = 1 2 ₀^ 4 d x ( 1 2 x+ 1 2 )^2 = & 1 2 ₀^ 4 d x ( cas ^2 ( 4 -x ) . = 1 2 ₀^ 4 ^2 ( 4 x ) d x = & 1 2 [- ( 4 -x ) ]₀^ 4 = -1 2 [ 0- 4 ] = & -1 2 [0- 1 2 ]= 1 2 aligned

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