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 Mechanics - Question 1 - 2020 - Paper 3

To solve for [\int_{0}^{10} (f(x) + 1) , dx], we can use the property of integrals that allows us to separate the integrals of a sum:

[\int_{0}^{10} (f(x) + 1) , dx = \int_{0}^{10} f(x) , dx + \int_{0}^{10} 1 , dx]

From the question, we know that [\int_{0}^{10} f(x) , dx = 7].

Next, we need to compute [\int_{0}^{10} 1 , dx], which represents the area under the constant function 1 from 0 to 10. This is calculated as:

[\int_{0}^{10} 1 , dx = 1 \times (10 - 0) = 10]

Therefore, putting everything together:

[\int_{0}^{10} (f(x) + 1) , dx = 7 + 10 = 17]

Thus, the value is [17].