Prove that f (x)= {(2x+1, when 1≤ x≤2) , (x^2+1, when 2 ≤ x ≤3) , show that ∫ f(x)dx=34/3.,x ∈[1,3]

Question

Prove that

\(f(x) = \begin{cases} 2x+1, & \quad \text{when } 0 \le x\le2\\ x^2+1, & \quad \text{when} \,2\le x\le3 \end{cases}\)

Show that \(\int\limits_1^3(x)dx=\cfrac{34}{3}\) 

f (x)= {(2x+1, when 1≤ x≤2) , 

         (x²+1, when 2 ≤ x ≤3)

 ∫ f(x)dx=34/3.,x ∈[1,3]

Answer 1

 

\(=\cfrac{34}{3}\)