anonymous one year ago Last Question of the day The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Approximation, using the 4 intervals between those given points. x 4 9 11 14 15 f(x) –6 –11 –18 –21 –25

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1. anonymous

okay so i'v done this a couple of times but i keep getting the wrong answer.

2. SolomonZelman

you have a bunch of trapezoids, that is all. Area of each trapezoid is: $$\large\displaystyle A=(\Delta x)(h_1+h_2)/2$$ where $$\Delta x$$ is the width and $$\large\displaystyle (h_1+h_2)/2$$ is the average height $$\large\displaystyle Trapezoid_1=(9-4)(-6+-11)/2$$ $$\large\displaystyle Trapezoid_2=(11-9)(-18+-11)/2$$ $$\large\displaystyle Trapezoid_3=(14-11)(-21+-18)/2$$ $$\large\displaystyle Trapezoid_4=(15-14)(-25+-21)/2$$

3. SolomonZelman

4. SolomonZelman

Dont wonder the area is negative, that is because the entire thing is under the x-axis.

5. anonymous

yep im getting the same answer i was getting before , still wrong

6. anonymous

these are my answer choices –12.727 –11.546 –16.273 –13.909

7. anonymous

@SolomonZelman you still there ?

8. SolomonZelman

yes, i am here. I am just glitching outside the US a little.

9. SolomonZelman

what did you get when you added the trapezoids?

10. anonymous

153, i did the same thing but by taking the left point and right point sum and averaging them

11. SolomonZelman

Yes, the area of the trapezoid is given by the product of its average height times the width, and the area of your full shape is the sum of all trapezoids... i dont understand why these options are here.

12. SolomonZelman

i get -153 doing a completely valid method.... maybe your table has typos?

13. anonymous

perhaps we're finding the wrong thing . it says find the average value might mean the average slope not average area under the curve

14. anonymous

@ganeshie8 any idea?

15. freckles

$\frac{1}{b-a} \int\limits _a^b f(x) dx$

16. JoannaBlackwelder

The average function value formula is:|dw:1439414018001:dw|

17. freckles

is average value of a function on interval [a,b]

18. SolomonZelman

oh the area, sorry....

19. SolomonZelman

the average is what they need...

20. freckles

so you made it this far: $\frac{1}{15-4} \int\limits_4^{16} f(x) dx \\ \frac{1}{15-4}(-153)$

21. freckles

yes that 16 is suppose to be a 15

22. anonymous

okay im getting 13.909 looks right thank you @freckles

23. freckles

well -13.909 but yah

24. anonymous