Given that $$\int_0^{10} f(x) \,dx = 7$$ deduce the value of $$\int_0^{10} (f(x) + 1) \,dx$$ Circle your answer. - AQA - A-Level Maths Pure - Question 1 - 2020 - Paper 3

To deduce the value of the integral $\int_0^{10} (f(x) + 1) \,dx$, we can use the properties of integrals:

1. Break down the integral: We can express the integral as: $\int_0^{10} (f(x) + 1) \,dx = \int_0^{10} f(x) \,dx + \int_0^{10} 1 \,dx$

2. Evaluate the first part: From the information given, we have: $\int_0^{10} f(x) \,dx = 7$

3. Evaluate the second part: The integral of 1 over the interval from 0 to 10 is simply the length of the interval: $\int_0^{10} 1 \,dx = 10 - 0 = 10$

4. Combine the results: Now we combine the two results: $\int_0^{10} (f(x) + 1) \,dx = 7 + 10 = 17$

Thus, the value of the integral is 17. Therefore, the correct answer is 17.