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MHT CET202619 April 2026Evening ShiftMathematicsDefinite IntegrationActual

If f(x) = |5x - 3| is defined on interval [0, 1] , then the value of ₀^1 f(x) ,dx is...

Options

  1. A13 10
  2. B9 10
  3. C3 10
  4. D17 10

Correct answer

A. 13 10

Step-by-step solution

Let I = ₀^1 |5x - 3| , dx The expression 5x - 3 changes sign at x = 3 5 . Splitting the integral at this point: I = ₀^ 3/5 (3 - 5x) , dx + _ 3/5 ^1 (5x - 3) , dx I = [ 3x - 5x^2 2 ]₀^ 3/5 + [ 5x^2 2 - 3x ]_ 3/5 ^1 I = ( 3 ( 3 5 ) - 5 2 ( 9 25 ) ) + ( ( 5 2 - 3 ) - ( 5 2 ( 9 25 ) - 3 ( 3 5 ) ) ) I = ( 9 5 - 9 10 ) + ( - 1 2 - ( 9 10 - 9 5 ) ) I = 9 10 + ( - 1 2 + 9 10 ) I = 9 10 + 4 10 = 13 10 Answer: 13 10

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