Find 10k where k is the area of the region x≥0, x+y≤3, x²≤4y and y≤1+√x.
Physics · Mixed Chapter
JEE Main Practice

Question

Find 10k where k is the area of the region x≥0, x+y≤3, x²≤4y and y≤1+√x.

G1 Physics · Accepted Answer

Step 1: The inequalities become y≥x²/4 and y≤min(3−x,1+√x). Step 2: Upper boundaries meet at x=1: 3−x=1+√x. Lower parabola meets upper line 3−x at x=2. Step 3: Area k=∫₀¹(1+√x−x²/4)dx + ∫₁²(3−x−x²/4)dx. Step 4: First integral=19/12; second integral=11/12; total k=30/12=2.5 square units. Step 5: Hence 10k=25, contradicting the original PDF key 4; the region statement or key is erroneous.