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MHT CET202620 April 2026Evening ShiftMathematicsDefinite IntegrationActual

If _ - /2 ^ /2 ( ^2 x + ^3 x)dx = k , then the value of k

Options

  1. A0
  2. B1
  3. C2

Correct answer

3

Step-by-step solution

Let I = _ - /2 ^ /2 ( ^2 x + ^3 x) dx I = _ - /2 ^ /2 ^2 x dx + _ - /2 ^ /2 ^3 x dx Since ^3 x is an odd function, _ - /2 ^ /2 ^3 x dx = 0 Since ^2 x is an even function, _ - /2 ^ /2 ^2 x dx = 2 ₀^ /2 ^2 x dx I = 2 ₀^ /2 ^2 x dx = 2 ( 4 ) = 2 Therefore, k = 2 Answer: 2

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