(i) Evaluate ∫1/x(1+ logx)^2 dx, x ∈ [1,2] (ii) Evaluate ∫ (2x^2 + 3)dx, x ∈ [0,3]

Question

(i) Evaluate \(\int\limits_1^2 \frac{1}{x(log +logx)^2}\) dx

(ii) Evaluate \(\int\limits_0^3 (2x^2 + 3)dx\) as the limit of a sum

Answer 1

(ii) Here the function is f(x) = 2x² + 3, a = 0, b = 3 and h = \(\frac{b - a}{n} = \frac{3}{n}\)