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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)

    \frac{39}{16}

  • Option 2)

    \frac{9}{8}

  • Option 3)

    \frac{13}{3}

  • Option 4)

    \frac{13}{6}

 
Answers (1)
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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