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MHT CET202313 May 2023Evening ShiftMathematicsArea Under CurvesActual

If a curve y= a x + b x passes through the point (1,2) and the area bounded by the curve, line x=4 and X -axis is 8 sq. units, then

Options

  1. Aa =3, ~b =-1
  2. Ba =3, ~b =1
  3. Ca =-3, ~b =1
  4. Da =-3, ~b =-1

Correct answer

A. a =3, ~b =-1

Step-by-step solution

The given curve passes through (1,2) . 2=a+b According to the given condition, ₀^4(a x +b x) d x=8 ...(i) 2 a 3 [x^ 3 / 2 ]₀^4+ b 2 [x^2 ]₀^4=8 2 a 3 8+8 ~b =8 2 a+3 b=3 ...(ii) From (i) and (ii), we get a =3, ~b =-1

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