Question

Why is C the answer for this question?

Answer 1

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 = (b-a)/(n) \ and\ x_(k)=a+\Delta x * (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).