Note that the curve is above the x-axis from x = 1 to x = and below the x-axis from x = to
x = 2. Thus, we need to evaluate two integrals to find the area.
cos x dx + (− cos x) dx
We will need a calculator to evaluate these integrals.
cos x dx + (−cos x)dx ≈ 0.249
44. D First, we find ∫cot x dx by rewriting the integral as .
Then, we use u-substitution. Let u = sin x and du = cos x.
Substituting, we can get = ln|u| + C. Then substituting back, we get ln(sin
x) + C. (We can get rid of the absolute value bars because sine is always positive on the
interval.)
Next, we use f = 1 to solve for C. We get 1 = ln + C.
