Answer: B and C are equivalent.
- A sec x + C, a differentiation result mistaken for integration
- B ln|sec x| + C, missing the equivalent cosine form
- C -ln|cos x| + C, missing the equivalent secant form
- D B and C are equivalent
Correct answer: D. B and C are equivalent
Explanation: tan x = sin x / cos x. Integral = -ln|cos x| + C = ln|sec x| + C. Both B and C are correct.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.