SOLUTION: Find the area under the curve defined by the following data points: x 1 4 7 10 13 16 19 22 25 y 2.6 4.6 5.1 6.2 7.3 7.8 9.2 8.8 9.4 Round your answer to 2 decimal places.

Question 1115239: Find the area under the curve defined by the following data points:
x 1 4 7 10 13 16 19 22 25
y 2.6 4.6 5.1 6.2 7.3 7.8 9.2 8.8 9.4
Round your answer to 2 decimal places.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
use the trapezoidal rule for finding the area under a curve from its coordinates
:
area = delta x * (y0/2 + y1 + y2 ....+ yn/2), where delta x = (xn - x0) / n
:
delta x = (25 - 1) / 8 = 3
:
area = 3 * (2.6/2 + 4.6 + 5.1 + 6.2 + 7.3 + 7.8 + 9.2 + 8.8 + 9.4/2) = 165.00
:
Note this formula works as long as we have the same value for each x-step
:
Consider simpson's rule
:
area = (delta x / 3) * (y0 + 4*y1 + 2*y2 + 4*y3 + 2*y4 + .... + yn)
:
area = 1 * (2.6 + 4*4.6 + 2*5.1 + 4*6.2 + 2*7.3 + 4*7.8 + 2*9.2 + 4*8.8 + 9.4) = 164.80
:
Usually Simpson's rule gives a better estimate for the area under the curve
:
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