If the area between y=m x² and x=m y²(m>0) is 1 / 4 sq units, then the value of m is

Step-by-step solution

Given curves; y=m x² and y² m=x ; m>0 Intersection point of both curves; x=m (m x² )²=m³ x⁴ m³ x⁴-x=0 array cc & x (m³ x³-1 )=0 & x(m x-1) (m² x²+1+m x )=0 & x=0, x=1 / m and y=0, y=1 / m array We take only the points =(0,0) and (1 / m, 1 / m) Now, the area of the curve aligned &= ₀^ 1 / m ( x m -m x² ) d x Given, 1 4 &= [ 2 3 m x^ 3 / 2 -m x³ 3 ]₀^ 1 / m 1 4 &= [ 2 3 m 1 m^ 3 / 2 - m 3 1 m₃ ] 1 4 &= 2 3 m² - 1 3 m² 1 4 &= 1 3 m² m²= 4 3 m= 2 3 aligned