Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
![\int\limits^b_a {f(x)} \, dx \approx \sum\limits_{k=1}^{n}f(x_{k}) \Delta x \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times (k-1)](https://tex.z-dn.net/?f=%5Cint%5Climits%5Eb_a%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5Capprox%20%5Csum%5Climits_%7Bk%3D1%7D%5E%7Bn%7Df%28x_%7Bk%7D%29%20%5CDelta%20x%20%5C%5Cwhere%5C%20%5CDelta%20x%20%3D%20%5Cfrac%7Bb-a%7D%7Bn%7D%20%5C%20and%5C%20x_%7Bk%7D%3Da%2B%5CDelta%20x%20%5Ctimes%20%28k-1%29)
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
Answer: 1 73/90 if the decimal is 1.81 and the one is repeating
If the .81 is repeating then 1 9/11
Step-by-step explanation:
Answer:
The answer is -15.
Step-by-step explanation:
1. 2x - 1
2. 2(-7) - 1
3. (-14) - 1
4. -15
By plugging in our x value, we are able to use PEMDAS to multiply 2 and the value of x and then, we subtract 1 from the value we got from step 3 to get -15.
Answer: k = 55 degrees
Step-by-step explanation:
to find J, subtract 122 from 180, you get 58. The total number of degrees is 180. Since L is given as 67, and 67+58=125. Simply subtract 125 from 180 which is 55 degrees