Question

Find the indefinite integral:

∫ sin(s - 7) ds

(1) [(s² - 49)/2] * ln(s - 7) - (s² + 14s)/2 + C

(2) [(s² - 49)/2] * ln(s - 7) + (s² + 14s)/2 + C

Answer 1

None of the provided options correctly represent the indefinite integral of sin(s - 7), which should be -cos(s - 7) + C.

Step-by-step explanation:

The student has asked to find the indefinite integral of ∫ sin(s - 7) ds. To solve this, we would normally use a substitution method or recognize it directly as the derivative of a cosine function because the integral of sin(x) is -cos(x). However, the given options include a logarithmic function and a polynomial, which suggests a much more complicated integral or possible error because these do not appear to correspond to the integral of a simple sine function. Therefore, the correct indefinite integral of sin(s - 7) would be -cos(s - 7) + C, where C represents the constant of integration. None of the provided options are correct.