Question

You are given the following pieces of information: ∫₅² f(x) dx = -53, ∫₁³ f(x) dx = -9, ∫₉³² f(x) dx = 68. What is the value of ∫₁³ f(x) dx?

Answer 1

To find the value of the definite integral ∫₁³ f(x) dx, we can use the given information and the properties of definite integrals.

Step-by-step explanation:

To find the value of ∫13 f(x) dx, we can use the given information and the properties of definite integrals. From the given information, we know that ∫52 f(x) dx = -53 and ∫932 f(x) dx = 68. We can use the properties of definite integrals to rewrite the integral as: ∫13 f(x) dx = ∫52 f(x) dx - ∫932 f(x) dx.

Now we substitute the given values: ∫13 f(x) dx = -53 - 68 = -121.

Therefore, the value of ∫13 f(x) dx is -121.