Suppose the integral from 2 to 8 of g of x, dx equals 13, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of 2 plus the integral from 2 to 6 of g of x, dx.
16
18
8
32
note that
∫[2,6] + ∫[6,8] = ∫[2,8]
To find the value of 2 plus the integral from 2 to 6 of g(x), dx, we need to use the properties of definite integrals.
Given that the integral from 2 to 8 of g(x), dx equals 13, and the integral from 6 to 8 of g(x), dx equals -3, we can split the integral from 2 to 8 into two separate integrals:
∫[2 to 8] g(x), dx = ∫[2 to 6] g(x), dx + ∫[6 to 8] g(x), dx
Since we want to find the value of 2 plus the integral from 2 to 6 of g(x), dx, we can rewrite the equation as:
2 + ∫[2 to 6] g(x), dx = ∫[2 to 8] g(x), dx - ∫[6 to 8] g(x), dx
Now, substitute the given values into the equation:
2 + ∫[2 to 6] g(x), dx = 13 - (-3)
Simplifying, we get:
2 + ∫[2 to 6] g(x), dx = 13 + 3
2 + ∫[2 to 6] g(x), dx = 16
Therefore, the value of 2 plus the integral from 2 to 6 of g(x), dx is 16.