Question

Please please help 100 points

Answer 1

We're given

`\displaystyle \int_4^(-10) g(x) \, dx = -3`

which immediately tells us that

`\displaystyle \int_(-10)^4 g(x) \, dx = 3`

In other words, swapping the limits of the integral negates its value.

Also,

`\displaystyle \int_4^6 g(x) \, dx = 5`

The integral we want to compute is

`\displaystyle \int_(-10)^6 g(x) \, dx`

which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is

`\displaystyle \int_(-10)^6 g(x) \, dx = \int_(-10)^4 g(x) \, dx + \int_4^6 g(x) \, dx = 3 + 5 = \boxed{8}`