contestada

suppose that g is a continuous function, 3_integral^5
g(x)dx=18, and 3_integral^10 g(x)dx =36. Find
5_ integral^10 g(x)dx
those are intergral symbols with numbers on
top and bottom. please show work. thanks

Respuesta :

oladayoademosu

The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

The question has to do with definite integrals

What are definite integrals?

Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.

Given that

  • [tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex] and also
  •  [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex] and we require
  • [tex]\int\limits^{10}_5 {g(x)} \, dx[/tex]

For any integral  [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]

So,  [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]

So,   [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

Since

  • [tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex]and  
  • [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex]

Substituting the values of the variables into the equation, we have

[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

Learn more about definite integrals here:

https://brainly.com/question/24353968

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