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Need clarity, kindly explain! - Integral Calculus - JEE Main-18

If the line, y=mx, bisects the area of the region

\left \{ \left ( x,y \right ):0\leq x\leq \frac{3}{2},0\leq y\leq 1+4x-x^{2} \right \},then m equals :

  • Option 1)


  • Option 2)


  • Option 3)


  • Option 4)


Answers (1)


Geometrical interpretation of a definite integral -

An algebraic sum of the area of the figure bounded by the curve y = f(x), the x axis and the striaght lines x=a and x=b. The areas above x axis are taken as positive and the areas below x axis are taken as negative.  

- wherein

Where a< b