# Definite Integration: int[3,9][f(x)]dx = 7; find int[3,9][2*f(x) + 1]dx

#### sojeee

##### New member
Given that ∫ (9 upper limit and 3 lower limit) f(x) dx = 7
Evaluate
∫ (9 upper limit and 3 lower limit) 2f(x) +1 dx

Have no idea where to start

#### Subhotosh Khan

##### Super Moderator
Staff member
Given that ∫ (9 upper limit and 3 lower limit) f(x) dx = 7
Evaluate
∫ (9 upper limit and 3 lower limit) 2f(x) +1 dx

Have no idea where to start
$$\displaystyle \displaystyle{\int [a * f(x)]dx \ = \ a * \int f(x)dx}$$

#### sojeee

##### New member
$$\displaystyle \displaystyle{\int [a * f(x)]dx \ = \ a * \int f(x)dx}$$

Could u please explain this

#### pka

##### Elite Member
Given that ∫ (9 upper limit and 3 lower limit) f(x) dx = 7
Evaluate
∫ (9 upper limit and 3 lower limit) 2f(x) +1 dx
Have no idea where to start
I find your lack of grouping symbols makes this hard to read.
If this is a correct reading then: $$\displaystyle \large{\int_3^9 {(2f(x) + 1)dx} = 2\int_3^9 {f(x)dx + } \int_3^9 {1dx} }$$

#### Jomo

##### Elite Member
Could u please explain this
You can factor out any constant in front of the integral sign!