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.
2 times 2^30 simple means
that = (2^1) x (2^30)
<span>In multiplying numbers of the same base (in this case 2), the
exponents are just added, therefore giving us:
</span>
(2^1) x (2^30) = (2^31)
Answer:
<span>2 to the 31 power</span>
1) First, solve one linear equation for y in terms of x .
2) Then substitute that expression for y in the other linear equation.
3)Solve this, and you have the x -coordinate of the intersection.
4)Then plug in x to either equation to find the corresponding y -coordinate.
Answer:
ft if
Step-by-step explanation:
good morning I am not sure if you have received this email is strictly confidential and may be a good time
Answer:
6
Step-by-step explanation:
because 6 sub 5 is equal to 1
