Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
Question 1 Report
Find the area between line y = x + 1 and the x-axis from x = -2 to x = 0.
Answer Details
To find the area between the line y = x + 1 and the x-axis from x = -2 to x = 0, we need to integrate the equation of the line with respect to x over the interval [-2, 0] and take the absolute value of the result.
The equation of the line y = x + 1 can be rewritten as x = y - 1, which gives us a different way to represent the line. Integrating this expression with respect to x over the interval [-2, 0] gives:
∫[-2,0] (y - 1) dx = [xy - x] from -2 to 0 = (0-0) - (-2*(-1)) = 2
Taking the absolute value of this result gives us an area of 2 square units.
Therefore, the answer is 2 square units.
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