The area of the region bounded by the curve y = 2x + 1 and the lines x = -2 and x = 0 is?
Answers
Answer:
Correct option is
A
9sq. units
We have to find area of the region bounded by curves y=x
2
+1 and y=2x−2 between x=−1andx=2
To find points of intersections, if any, for the parabola and the straight line we solve both simultaneously.
x
2
+1=2x−2
⇒x
2
−2x+3=0, which has no real solutions. Hence, no points of intersection for the parabola and the straight line.
From the figure, the graph of y=x
2
+1 will be always above the graph of y=2x−2.
Hence the required area is
−1
∫
2
[(x
2
+1)−(2x−2)]dx
−1
∫
2
(x
2
−2x+3)dx
=
3
x
3
∣
−1
2
−x
2
∣
−1
2
+3x∣
−1
2
=3−(3)+9
=9squnits.
Step-by-step explanation:
To find the area of the region bounded by the curve y = 2x + 1 and the lines x = -2 and x = 0, we need to integrate the equation of the curve between the given limits of x.
The curve y = 2x + 1 intersects the x-axis at the point (-1/2, 0).
The area of the region bounded by the curve y = 2x + 1 and the lines x = -2 and x = 0 can be calculated as:
Area = Integral from -2 to 0 of (2x + 1) dx
= [x^2 + x] from -2 to 0
= (0^2 + 0) - (-2^2 + (-2))
= 4
Therefore, the area of the region bounded by the curve y = 2x + 1 and the lines x = -2 and x = 0 is 4 square units.