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MHT CET20255 May 2025Evening ShiftMathematicsIndefinite IntegrationActual

7 x 9 x 2 x ~d x is equal to

Options

  1. A(9 x)- (2 x)+c , where c is the constant of integration
  2. B(9 x)+ (2 x)+c, where c is the constant of integration
  3. C1 9 (9 x)- 1 2 (2 x)+c , where c is the constant of integration
  4. D1 9 (9 x)+ 1 2 (2 x)+c , where c is the constant of integration

Correct answer

C. 1 9 (9 x)- 1 2 (2 x)+c , where c is the constant of integration

Step-by-step solution

A thorough comprehension of the angles allows rewriting the numerator: since 7x = 9x - 2x , employing the identity (A - B) = A B - A B gives 7x = 9x 2x - 9x 2x . Substituting into the integral, 7x 9x 2x dx = 9x 2x - 9x 2x 9x 2x dx . Splitting the integrand, this becomes ( 9x 9x - 2x 2x ) dx = ( 9x - 2x) dx . The standard integrals yield ax dx = 1 a | ax| + C , so combining terms gives the anti-derivative 1 9 | 9x| - 1 2 | 2x| + C . This matches option C. Final answer: C

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