1. **State the problem:** We are given two definite integrals: $$\int_{-1}^4 f(x) \, dx = -2$$ and $$\int_{-1}^4 g(x) \, dx = 9$$ We need to find the value of: $$\int_{-1}^4 (f(x) - 4g(x)) \, dx$$ rounded to the nearest integer. 2. **Recall the properties of definite integrals:** The integral of a sum/difference is the sum/difference of the integrals: $$\int_a^b [f(x) \pm g(x)] \, dx = \int_a^b f(x) \, dx \pm \int_a^b g(x) \, dx$$ Also, constants can be factored out: $$\int_a^b c \cdot g(x) \, dx = c \int_a^b g(x) \, dx$$ 3. **Apply these properties:** $$\int_{-1}^4 (f(x) - 4g(x)) \, dx = \int_{-1}^4 f(x) \, dx - 4 \int_{-1}^4 g(x) \, dx$$ 4. **Substitute the given values:** $$= -2 - 4 \times 9$$ 5. **Calculate:** $$= -2 - 36 = -38$$ 6. **Final answer:** The value of the integral is **-38** (already an integer, so no rounding needed).