Question

Calculate R8 for f(x)=6−x over 3,5

Answer 1

The integration of the given function over 3 to 5 is 8.

Explanation:

we have to find the integration of a function f(x)=6-x from 3 to 5 i.e. we need to find definite integration of the function f(x)=6-x.

`\int_(3)^(5)6-x=6\cdot5-(25)/(2)-6\cdot3+(9)/(2)`

`\int_(3)^(5)6-x=30-(25)/(2)-18+(9)/(2)`

`\int_(3)^(5)6-x=30-18-(25)/(2)+(9)/(2)`

`\int_(3)^(5)6-x=12-8=4`

Hence, the desired result is 8.

Answer 2

We are given
f(x) = 6 - x
and we are asked for the definite integral over 3, 5

Taking the integral
∫f(x) = 6x - x²/2
applying the limits
6(3) - 6²/2 - (6(5) - 5²/2)
The answer is 17.5