Question

Let f(x) = (1 – x)²sin²x + x² for all x in R and g(x) = ∫(2(t – 1)/(t + 1) – lnt)f(t)dt for t∈[1, x] for all x > 1. which of the following is true?

(a) g is inc. on (1, ∞)

(b) g is dec. on (1, ∞)

(c) g is inc. on (1, 2) and dec. on (2, ∞)

(d) g is dec. on (1, 2) and inc. on (2, ∞).

Answer 1

Correct option (b) g is dec. on (1, ∞)   

Explanation:

So h(x) < 0 for all x > 1

Thus, g(x) is decreasing on (1, ∞).