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NDA2020MathematicsDefinite IntegrationActual

What is the value of ₀^ / 4 ( ^3 x+ x ) d x ?

Options

  1. A1 4
  2. B1 2
  3. C1
  4. D2

Correct answer

B. 1 2

Step-by-step solution

aligned I & = ₀^ 4 ( ^3 x+ x ) d x & = ₀^ 4 ^3 x d x+ ₀^ 4 x d x aligned aligned & = ₀^ 4 x ^2 x d x+ ₀^ 4 x d x = & ₀^ 4 x ( ^2 x-1 ) d x+ ₀^ 4 x d x aligned aligned & = ₀^ 4 x ^2 x d x- ₀^ 4 x d x+ ₀^ 4 x d x & = ₀^ 4 x ^2 x d x aligned aligned & Let x=z, d z= ^2 x d x & x ^2 x d x= z d z= z^2 2 +C aligned where C= constant I= [ ^2 x 2 ]₀^ 4 = 1 2 -0= 1 2 .

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