Find the particular antiderivative that satisfies the following conditions:

Question

R′(x)=2−0.5x;R(0)=1

Answer 1

R'(x) = 2 - 0.5x   R(0) = 1

 

R(x) = ∫ R'(x)dx

 

       = ∫(2 - 0.5x)dx

 

       = 2x - 0.25x² + C

 

Since R(0) = 1, we have 0 - 0 + C = 1.  So, C = 1

 

R(x) = 2x - 0.25x² + 1