Question

How do you evaluate the definite integral `int (x^2+4x+4)dx` from [0,2]?

Answer 1

`56/3`.

Explanation:

Start by integrating using the rule `int(x^n)dx= x^(n + 1)/(n + 1) + C`.

`int_0^2(x^2 + 4x + 4)dx = 1/3x^3 + 2x^2 + 4x|_0^2`

We now use the rule that `int_a^b f(x) dx = F(b) - F(a)`, where `F(x)` is the antiderivative of `f(x)`.

`=>1/3(2)^3 + 2(2)^2 + 4(2) - (2/3(0)^3 + 2(0)^2 + 4(0))`

`=>1/3(8) + 8 + 8 - 0`

`=>56/3`

Hopefully this helps!