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COMEDK2018MathematicsDefinite Integration

The value of _ -2 ² (a x³+b x+c ) d x depends on the

Options

  1. Avalue of b
  2. Bvalue of c
  3. Cvalue of a
  4. Dvalues of a and b

Correct answer

B. value of c

Step-by-step solution

aligned Let I &= _ -2 ² (a x³+b x+c ) d x &= _ -2 ² (a(-2+2-x)³+b(-2+2) x+c ) d x [ _ a ^ b f(x) d x= _ a ^ b f(a+b-x) d x ] I= _ -2 ² (-a x³-b x+c ) d x aligned On adding Eqs. (i) and (ii), we get aligned 2 I &= _ -2 ² 2 c d x I &=4 c aligned So, value of I depends on the value of c .

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