Final answer:
To find the integral of f(x) from 1 to 6, use the additivity property of integrals and the given values for the integrals from 1 to 7 and from 6 to 7. Subtract the latter from the former to get 1∫6 f(x) dx = 2.9.
Step-by-step explanation:
The question asks to find the value of the integral from 1 to 6 of the function f(x), given that the integral from 1 to 7 is 8.1 and the integral from 6 to 7 is 5.2.
This is a problem that uses the properties of definite integrals, specifically that the integral of a function over an interval can be found by splitting the interval and using the additivity property of the integrals.
To solve the problem, we utilize the following relationship: integral from 1 to 7 = integral from 1 to 6 + integral from 6 to 7. Using the values given:
₁∫⁷ f(x) dx = ₁∫⁶ f(x) dx + ₆∫⁷ f(x) dx
8.1 = ₁∫⁶ f(x) dx + 5.2
By subtracting 5.2 from both sides of the equation, we obtain:
₁∫⁶ f(x) dx = 8.1 - 5.2
₁∫⁶ f(x) dx = 2.9
Thus, the value of the integral from 1 to 6 of f(x) is 2.9.