Question

Help with this calc question?

Answer 1

Option `B`, which is `18`, will be correct.

Explanation:

One of the properties of definite integrals states that

`int_a^cf(x)dx= int_a^bf(x)dx + int_b^cf(x)dx` if `a ≤ b ≤ c`

We can apply that to this problem. We know that

`int_2^8g(x) dx = int_2^6 g(x)dx+ int_6^8g(x)dx`

Two of the integral values are known, it's just a matter of solving for the third.

`13 = int_2^6 g(x)dx - 3`

`16 = int_2^6g(x)dx`

Now add the constant.

`2 + 16 = 18`

Hopefully this helps!