Find F as a function of x

Question

The question states: 

 

F(x)= int_1^x(t³+7t-6)dt

 

( F(x) is the integral of (t³+7t-6)dt from x to 1)

Answer 1

 

Hi Abigail,

 

F(x) = ∫₁^x (t³ + 7t - 6) dt

 

       = [t⁴/4 + 7t²/2 - 6t]₁^x

 

       = (x⁴/4 + 7x²/2 - 6x) - (1⁴/4 + 7·1²/2 - 6·1)

 

       = (x⁴/4 + 7x²/2 - 6x) - (-9/4)

 

       = x⁴/4 + 7x²/2 - 6x + 9/4