hw 9 question 8

Question

Integrate (using substitution) and evaluate to 4 decimal places.

Answer 1

= integral of du/u = lnu = ln(x^4 +2x) 4x^3 + 2 is the derivative of x^4+2x

evaluate at x= 3 and x= 1

ln(81+6) - ln(1+2) = ln87 - ln3 = ln(87/3) = ln29

use a calculator to get ln29 = 3.3673 rounded off to 4 decimals

Answer 2

hi,

u(x ) = x^4 + 2x -----> du = (4x^3 + 2 ) dx

back to question:

= ∫ du/u = Ln(u) = Ln( x^4 + 2x ) + c then replace x = 3 , x = 1------.>

= Ln( 3^4 + 2*3 ) - Ln( 1+2) = Ln(87) - Ln(3) = Ln(87/3) = Ln29

I hope it is useful,

Minoo