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kolezko [41]
3 years ago
13

Why is C the answer for this question?

Mathematics
1 answer:
Grace [21]3 years ago
8 0

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)

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).

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