Question

Evaluate. S (12 +7+-5) dt 0 24 + 7 + c 61 + 712.5t +C 0 121 + 712 - 5t + c O 4 + 2 / 12.51 +6

Answer 1

Antiderivative

The antiderivative of a function f(x) is another function F(x) such that:

f(x)=F'(x)

The most-used antiderivative is the so-called reverse power rule:

`\int x^ndx=(x^(n+1))/(n+1)+C`

We have to compute:

`\int (12t^2+7t-5)\text{ dt}`

Separating the integrals:

`\int 12t^2\text{ dt}+\int 7t\text{ dt}-\int 5\text{ dt}`

Apply the rule above:

`(12t^3)/(3)+7(t^2)/(2)-5t+C`

Simplifying:

`4t^3+(7)/(2)t^2-5t+C`

The last option is correct