Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of

x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16

are you fing dumb obvi he doesnt know he needs help

it isn't just finding the area of a trapezoid, it's estimating the area of a function by using trapezoids.

answer is 81

To estimate the value of the integral using trapezoids, we need to divide the interval into equal subintervals and approximate the area under the curve within each subinterval using trapezoids.

Since we are given 6 trapezoids, we need to divide the interval [1, 10] into 6 equal subintervals. The width of each subinterval can be calculated by dividing the total width of the interval by the number of subintervals:

Width of each subinterval = (Total width of interval) / (Number of subintervals)
= (10 - 1) / 6
= 9 / 6
= 1.5

Now, let's calculate the area of each trapezoid within the subintervals.

For the first trapezoid, the height is the average of the first two function values (4 + 8) divided by 2, and the width is 1.5.

Area of trapezoid 1 = (1.5 * ((4 + 8) / 2))
= 1.5 * (12 / 2)
= 1.5 * 6
= 9

For the second trapezoid, the height is the average of the second and third function values (8 + 6) divided by 2, and the width is 1.5.

Area of trapezoid 2 = (1.5 * ((8 + 6) / 2))
= 1.5 * (14 / 2)
= 1.5 * 7
= 10.5

Continue this process for the remaining trapezoids:

Area of trapezoid 3: (1.5 * ((6 + 10) / 2)) = 1.5 * (16 / 2) = 12
Area of trapezoid 4: (1.5 * ((10 + 10) / 2)) = 1.5 * (20 / 2) = 15
Area of trapezoid 5: (1.5 * ((10 + 12) / 2)) = 1.5 * (22 / 2) = 16.5
Area of trapezoid 6: (1.5 * ((12 + 16) / 2)) = 1.5 * (28 / 2) = 21

Finally, the estimate of the integral is the sum of the areas of the trapezoids:

Estimated integral = Area of trapezoid 1 + Area of trapezoid 2 + ... + Area of trapezoid 6
= 9 + 10.5 + 12 + 15 + 16.5 + 21
= 84

Therefore, the estimated value of the integral using 6 trapezoids is 84.

so, don't you know how to find the area of a trapezoid?