Question

Let g be a continuous function such that

₋₄∫ ⁴g(x)dx=8
₄∫¹⁴g(x)dx=13
Use this information to evaluate each of the following integrals.
₋₄ ∫¹⁴g(x)dx=

Answer 1

By utilizing the properties of integrals, the integral of g(x) from -4 to 14 is calculated by summing the given integrals over two intervals, yielding a result of 21.

Step-by-step explanation:

The student has provided the integral of a continuous function g(x) over the interval from -4 to +4 and also from 8 to 14, and we need to evaluate the integral from -4 to 14. The properties of integrals tell us that we can break the integral into two parts and sum them to find the desired result:

−4∫14 g(x)dx = (−4∫8 g(x)dx) + (8∫14 g(x)dx)

We are given:

• −4∫8 g(x)dx = 8
• 8∫14 g(x)dx = 13

By adding these two results:

8 + 13 = 21

Thus, we find that:

−4∫14 g(x)dx = 21