Answer: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. solution Step-by-step explanation: Reply
Answer: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.
solution
Step-by-step explanation: