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← JEE Main 2022 · 30 Jun · Shift 1
MathematicsInteger+4 / -1Question 24 of 90

JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 24

If for some α>0\alpha>0, the area of the region {(x,y):∣x+α∣≤y≤2−∣x∣}\{(x,y):|x+\alpha|\le y\le2-|x|\} is equal to 32\dfrac32, then the area of the region {(x,y):0≤y≤x+2α, ∣x∣≤1}\{(x,y):0\le y\le x+2\alpha,\ |x|\le1\} is equal to ______.

Answer and worked solution

Official answer: 4

First region. In u=y−xu=y-x, v=y+xv=y+x it is α≤u≤2\alpha\le u\le2, −α≤v≤2-\alpha\le v\le2: area (2−α)(2+α)2=32\frac{(2-\alpha)(2+\alpha)}2=\frac32, so α=1\alpha=1.

Second region. ∫−11(x+2)dx=4\int_{-1}^1(x+2)dx=4.

Answer: 4

Topics:Area between curvesInequalities and modulus
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