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JEE Main202522 Jan 2025Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let the function, f(x)= cases -3 a x^2-2, & x 1 a^2+b x, & x 1 cases be differentiable for all x R , where a 1, b R . If the area of the region enclosed by y=f(x) and the line y=-20 is + 3 , , Z , then the value of + is ________

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0

Step-by-step solution

f(x) is continuous and differentiable aligned & at x=1, LHL = RHL , LHD = RHD & -3 a-2=a^2+b,-6 a=b & a=2 ; b=-12 & f(x)= array cc -6 x^2-2, & x aligned & . Area = _ - 3 ^1 (-6 x^2-2+20 ) d x+ ₁^2(4-12 x+20) d x ] & =16+12 3 +6=22+12 3 & + =34 aligned

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