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Can someone please explain how to solve this? Write the limit as a definite integral on the interval [3, 7] where ciis any point on the i-th?
Write the limit as a definite integral on the interval [3, 7] where ci is any point on the i-th subinterval. lim n→∞∑n i=1 5ci(7+c2i)Δxi
1 Answer
- ?Lv 75 days ago
This is basically the Riemann sum of f(x) = 5x(7+x²).
Imagine breaking it up in n thin vertical strips from 3 to 7. [do draw this to get a better understanding of it].
The i'th strip has width Δxi. Take any x point in there & call it ci.
Thus f(ci) is roughly the height of the thin rectangle.
Adding all these thin rectangles from x=3 to 7 is ∑ 5ci(7+ci²)Δxi. Taking n --> infity, this is thus the integral of f(x) from 3 to 7...
