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NDA2024MathematicsDefinite IntegrationActual

What is _ -1 ^1(3 x- 3 x) ^2 x d x equal to?

Options

  1. A- 1 4
  2. B0
  3. C1 2
  4. D1 4

Correct answer

B. 0

Step-by-step solution

Let, I = _ -1 ^1(3 x- 3 x) ^2 x d x aligned I & = _ -1 ^1 (3 x-3 x+4 ^3 x ) ^2 x d x I & = _ -1 ^1 4 ^3 x ^2 x d x & = _ -1 ^1 f(x) d x aligned Here, f(x)=4 ^3 x ^2 x is an odd function as f(-x)=-f(x) I = _ -1 ^1 4 ^2 x ^2 x d x=0

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