Question

How do you evaluate the definite integral `int 2x+3` from `[1,3]`?

Answer 1

`14`

Explanation:

To evaluate `int_1^3(2x+3)dx`

integrate using the `color(blue)"power rule"`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(int(ax^n)dx=a/(n+1)x^(n+1))color(white)(a/a)|)))`

`rArrint_1^3(2x+3)dx=[x^2+3x]_1^3`

now evaluate function at upper limit and subtract the evaluation at the lower limit.

`rArr[x^2+3x]_1^3=(9+9)-(1+3)=18-4=14`