Question

Please help i’m begging

Answer 1

The answer is
`(725)/(3)` .

To calculate the integral

∫
`_4^8 (7x + x^2) dx`

given that

∫
`_4^8 x^2 dx` =
`(448)/(3)`

∫
`_0^9 x^2 dx` =
`(217)/(3)`

we can use the following steps:

Split the integral into two parts, one for the linear term and one for the quadratic term:

∫
`_4^8 (7x + x^2) dx` = ∫
`_4^8 7x dx` + ∫
`_4^8 x^2 dx`

Evaluate the first integral using the power rule:

∫
`_4^8 7x dx` =
`(7)/(2)`
`x^2` |
`_4^8` =
`(7)/(2)` (64 - 16) = 224

Evaluate the second integral using the given information:

∫
`_4^8 x^2 dx` = (
`(448)/(3)` ) - (
`(217)/(3)` ) =
`(77)/(3)`

Add the two results to find the final answer:

∫
`_4^8 (7x + x^2) dx` = 224 +
`(77)/(3)` =
`(725)/(3)`

Therefore, the answer is
`(725)/(3)` .