Calculate the integral below, assuming that ∫50f(x)dx=5∫05f(x)dx=5 and ∫50g(x)dx=12∫05g(x)dx=12. ∫50(6f(x)−13g(x))dx=

Question

Calculate the integral below, assuming that ∫50f(x)dx=5∫05f(x)dx=5 and ∫50g(x)dx=12∫05g(x)dx=12.

∫50(6f(x)−13g(x))dx=

Answer 1

50∫f(x)dx = 5         and                50∫g(x)dx = 12

 

∫50(6f(x) - 13g(x)) dx

 

 

The integral of the sum is the sum of integrals.  Also, any constant coefficient can be taken out of the integral.

 

300∫f(x)dx - 650∫g(x)dx =

 

6(5) - 13(12) =

 

30 - 156 =

 

-126