Question

How do you find the definite integral of `(3x^3 +7) dx` from `[1, 5]`?

Answer 1

496

Explanation:

`color(red)(|bar(ul(color(white)(a/a)color(black)(int_a^bf(x)dx=[F(x)]_a^b=F(b)-F(a))color(white)(a/a)|)))`

Integrate each term using the `color(blue)"power rule"`

`int(ax^n)dx=a/(n+1)x^(n+1)`

`rArrint_1^5(3x^3+7)dx=[3/4x^4+7x]_1^5`

`=(3/4(5)^4+7(5))-(3/4(1)^4+7(1))`

`=1875/4+35-3/4-7=1872/4+28=496`