Question

Suppose that g is a continuous function, 3_∫^5 g(x)dx=18, and

3_∫^10
g(x)dx =36. Find
5_ ∫^10 g(x)dx
those are intergral symbols with numbers on top and bottom. please
show work. thanks

Answer 1

18

Explanation:

Given:

`\int\limits^3_5 {g(x)} \, dx =18\\\\\int\limits^3_(10) {g(x)} \, dx =36`

We have:

`\int\limits^3_(10) {g(x)} \, dx = \int\limits^3_(5) {g(x)} \, dx+\int\limits^5_(10) {g(x)} \, dx`

⇒

`\int\limits^5_(10) {g(x)} \, dx = \int\limits^3_(10) {g(x)} \, dx-\int\limits^3_(5) {g(x)} \, dx`

⇒

`\int\limits^5_(10) {g(x)} \, dx = 36-18\\\\=18`