Use the form of the definition of the integral given in the theorem to evaluate the integral.

Question

1

(1 + 2x) dx

−1

Answer 1

1

(1 + 2x) dx = lim_n->∞∑ⁿ_i=1f(x_i)Δx

−1

Δx = (1-(-1)/n = 2/n x_i = -1+2/n

f(x_i) = (1-1+2i/n) = 2i/n

∑2i/n(2/n) = (4/n²)(n+1)n/2 = 2(1+1/n)

lim_{n->∞2(1+1/n) = 2(1+0) = 2}

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