Evaluate the integral

Question

∫₁⁴ ( (4 + 6u)/( u^1/2)) du

 

 

ANSWER: 36

#29, p404

Answer 1

∫(4+6u)/u^½du = 4∫u^-½du + 6∫u^½du

 

                      = 4 (2)u^½ + 6(2/3)u^3/2 

 

                      = 8u^½ + 4u^3/2

 

Evaluate from 1 to 4 to get:  

 

[8(4)^½+4(4)^3/2] - [(8)(1)^1/2+(4)(1)^3/2]

 

= 16 + 32 - 8 - 4   

 

= 36