evaluate the integral

Question

Upper limit of integral: T

Lower limit of integral: 2

Function of integral: (x^2+17)/x^2 dx

 

What is the integral equal to?

 

 

Answer 1

 

Hi Sydney,

 

     ∫^T₂ (x² + 17)/x² dx

 

            = ∫^T₂ (1 + 17/x²) dx

 

            = ∫^T₂ 1 dx + 17∫^T₂ (1/x²) dx

 

            = x|^T₂ +17·(-1/x)|^T₂           ( as d(1/x)/dx = -1/x², ∫(1/x²)dx = -1/x + C )

 

            = (T - 2) + 17·(-1/T - (-1/2))

 

            = T - (17/T) + (13/2)