1. Suppose that F and g are differentiable functions, with f = F′. Assuming that f and g′ are continuous, what is ∫ab f(g(x)) g′(x) dx?
2. Suppose you wish to integrate sin x cos x dx from x = 0 to x = π/2, using the substitution u = sin x (so that du = cos x dx). Explain the mistake in this calculation: ∫0π/2 sin x cos x dx = ∫0π/2 u du = (½u2)|0π/2 = ½(π/2)2 − ½(0)2 = π2/8. (The correct value of the integral is actually ½.)
1. Suppose that F and g are differentiable functions, with f = F′. Assuming that f and g′ are continuous, what is ∫ab
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1. Suppose that F and g are differentiable functions, with f = F′. Assuming that f and g′ are continuous, what is ∫ab
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