SOLUTION: Look at the following function https://ibb.co/PmMsknF The continuous function f is defined on the closed interval -6 less or equal than X less or equal than 5. The figure abo

Algebra ->  Rational-functions -> SOLUTION: Look at the following function https://ibb.co/PmMsknF The continuous function f is defined on the closed interval -6 less or equal than X less or equal than 5. The figure abo      Log On


   

Question 1192233: Look at the following function
https://ibb.co/PmMsknF
The continuous function f is defined on the closed interval -6 less or equal than X less or equal than 5. The figure above shows a portion of the graph of f, consisting of two lines segments and a quarter of a circle centered at the point (5,3). It is known that the point (3 , 3-sqrt(5)) is on the graph of f.
Link above already has PART A to be solved, please help me understand
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The integral of the function from -2 to 0 is 0, because there are equal areas above and below the x-axis. Likewise, the integral from 0 to 1 is 0.

So the integral of the function from -2 to 5 is equal to the integral from 1 to 5.

The integral from 1 to 2 is the area of a trapezoid of height 1 with bases 1 and 3; that area is 1%28%281%2B3%29%2F2%29=2.

The integral from 2 to 5 is the area of a 3x3 square, minus the area of the quarter circle, which is 9-%281%2F4%29%289pi%29.

So the integral from 1 to 5 of the function, and therefore the integral from -2 to 5, is 11-%289%2F4%29pi.

Then, given that the integral from -6 to 5 is 7, the integral from -6 to -2 is 7-%2811-%289%2F4%29pi%29+=+%289%2F4%29pi-4

ANSWER: %289%2F4%29pi-4