Question

Help now please i’m begging

Answer 1

The integral of 8x^2 from 5 to 8 is 1032.

The image shows a math problem asking to calculate (
`(\int_(5)^(8)8x^(2)dx`) given the following:

`\int_(5)^(7)x^(2)dx=(218)/(3)`

`\int_(7)^(8)x^(2)dx=(169)/(3)`

`\int_(5)^(5)8x^(2)dx=\Box`

We can solve this problem by using the following steps:

1. Split the integral into two parts:

`\int_(5)^(8)8x^(2)dx=\int_(5)^(7)8x^(2)dx+\int_(7)^(8)8x^(2)dx`

2. Simplify the integrals using the power rule:

`\int_(5)^(7)8x^(2)dx=8\int_(5)^(7)x^(2)dx=8\cdot(218)/(3)=(1744)/(3)\\\int_(7)^(8)8x^(2)dx=8\int_(7)^(8)x^(2)dx=8\cdot(169)/(3)=(1352)/(3)`

3. Add the two integrals to find the answer:

`\begin{aligned}\\\int_(5)^(8)8x^(2)dx&=\int_(5)^(7)8x^(2)dx+\int_(7)^(8)8x^(2)dx \\\\&=(1744)/(3)+(1352)/(3) \\\\&=(3096)/(3) \\\\&=\boxed{1032}\\\end{aligned}`

Therefore, the answer to the math problem is 1032.