Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider the functions f,g:RR defined by
f(x)=x2+512 and g(x)={2(14|x|3),|x|34,0,|x|>34.
If α is the area of the region
{(x,y)R×R:|x|34,0ymin{f(x),g(x)}},
then the value of 9α is _____

JEE AdvancedJEE Advanced 2022

Solution:

x2+512=28x3
x2+8x3+5122=0
image
12x2+32x19=0
12x2+38x6x19=0
2x(6x+19)1(6x+19)=0
(6x+19)(2x1)=0
x=12
α=2A1+A2
α=2(1/20x2+512dx+12×14×23)
α=2[(x33+5x12)1/20+112]
α=2[124+524+112]
α=2[1+5+224]α=2×8249α=9×812
9α=6