The area bounded by the lines \( y=1+|x+1|,x=-3,x=3 \) and \( y=0 \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16 Square units
Since \( 1+|x+1|\gt 0 \), the graph is above the x-axis. Split at x = −1:
\( \displaystyle \int_{-3}^{3}(1+|x+1|)\,dx=6+\int_{-3}^{-1}(-x-1)\,dx+\int_{-1}^{3}(x+1)\,dx \)
\( =6+2+8 \)
\( =16 \) square units
Shortcut: Area = rectangle of height 1 (area 6) + two triangles: base 2, height 2 (area 2) and base 4, height 4 (area 8). Total 16.