Suppose that a a) If f is continuous and nonnegative on [a, b] and g : [a, b] †’ [a, b] is differentiable and increasing on [a, b], then

is increasing on [a, b].
b) If f and g are differentiable on [a, b], if f' and g' are Riemann integrate on [a, b], and if f(a) = 0 but g is never zero on [a, b], then

for all x ˆˆ [a, b].
c) If f and g are differentiable on [a, b], and if f' and g' are Riemann integrable on [a, b], then

if and only if f(a)g(a) = f(b)g(b).
d) If f and g are continuously differentiable on [a, b], and if h is continuous on [a, b], then

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1460 fo) git) u g(r) f,(x)g(x) dx + f(x)g,(x) dx =0 gtf(b)) h(x) dx= | h(g(f(x)))g' (f(x)) f'(x) dx g(f(a)) 2