Split up the integration interval into 4 subintervals:
![\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac%5Cpi8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi8%2C%5Cdfrac%5Cpi4%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi4%2C%5Cdfrac%7B3%5Cpi%7D8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%7B3%5Cpi%7D8%2C%5Cdfrac%5Cpi2%5Cright%5D)
The left and right endpoints of the 
-th subinterval, respectively, are
for 
, and the respective midpoints are
We approximate the (signed) area under the curve over each subinterval by
so that
We approximate the area for each subinterval by
so that
We first interpolate the integrand over each subinterval by a quadratic polynomial 
, where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
Answer:
C is the answer
Step-by-step explanation:
Please mark brainliest
Answer:
can u zoom in ?????????????
Step-by-step explanation:
First expand the equation.
-5e+5+6e = -17
Next, combine the like terms.
e+5 = -17
e = -22
The given polyn. is not in std. form. To answer this question, we need to perform the indicated operations (mult., addn., subtrn.) first and then arrange the terms of this poly in descending order by powers of x:
P(x) = x(160 - x) - (100x + 500)
When this work has been done, we get P(x) = 160x - x^2 - 100x - 500, or
P(x) = -x^2 + 60x - 500
So, you see, the last term is -500. This means that if x = 0, not only is there no profit, but the company is "in the hole" for $500.
