Final answer:
The integral of f(x) from 1 to 3 is found to be 3.5 by utilising the additive property of definite integrals, subtracting the integral from 3 to 5 from the integral from 1 to 5.
Step-by-step explanation:
The student has asked to find the value of the integral ∫ f(x) dx from 1 to 3, given the integrals from 1 to 5 and from 3 to 5. To solve this, we'll use the properties of integrals, specifically the additive property of definite integrals. The additive property says that if you have an integral over a larger interval, you can break it down into the sum of integrals over smaller intervals.
Applying this property, we can express ∫_{1}^{5} f(x) dx as the sum of ∫_{1}^{3} f(x) dx and ∫_{3}^{5} f(x) dx. Since we know ∫_{1}^{5} f(x) dx = 9.1 and ∫_{3}^{5} f(x) dx = 5.6, we can solve for ∫_{1}^{3} f(x) dx:
∫_{1}^{3} f(x) dx = ∫_{1}^{5} f(x) dx - ∫_{3}^{5} f(x) dx
∫_{1}^{3} f(x) dx = 9.1 - 5.6
∫_{1}^{3} f(x) dx = 3.5
Thus, the value of the integral of f(x) from 1 to 3 is 3.5.