Question

Give the following information \[ z=\int_{4}^{-1} h(x) d x, \int_{4}^{7} h(x) d x=5, \int_{-1}^{7} h(x) d x=13 \] What does z equal?

Answer 1

By using the properties of definite integrals and the values provided, the value of z in the integral from 4 to -1 of h(x) is found to be 8.

Step-by-step explanation:

To determine what z equals given the information about the integrals of h(x), we can use the properties of definite integrals. The integral from 4 to -1 of h(x) can be thought of as subtracting the integral from -1 to 7 of h(x) from the integral of 4 to 7 of h(x).

Using the provided values:

• ∫_{4}^{7} h(x) dx = 5
• ∫_{-1}^{7} h(x) dx = 13

If we add the integral from 4 to -1 of h(x) to the integral from 4 to 7 of h(x), we should get the integral from -1 to 7 of h(x):

z + 5 = 13

So:

z = 13 - 5

z = 8