To find the area enclosed by the curve y = x + 1 between x = 1 and x = 3, we need to calculate the definite integral of the curve with respect to x within the given bounds.
First, rewrite the equation y = x + 1 in terms of x:
y = x + 1
Next, we will integrate the equation with respect to x from x = 1 to x = 3:
∫[1,3] (x + 1) dx
Integrating, we get:
= 1/2x^2 + x | [1,3]
= (1/2 * 3^2 + 3) - (1/2 * 1^2 + 1)
= (1/2 * 9 + 3) - (1/2 * 1 + 1)
= (4.5 + 3) - (0.5 + 1)
= 7.5 - 1.5
= 6
Therefore, the area enclosed by the curve y = x + 1 between x = 1 and x = 3 is 6 square units.
Find the area enclosed by the curve y=X+1 between X=1 and X= 3
1 answer