Evaluate the definite integral

Question

Evaluate the definite integral ∫(x^4+3x^7)/(x^5) dx [1,2]

Answer 1

Ana,

∫(x^4+3x^7)/(x^5) dx [1,2]

First, every term must be divided by x^5 It means:

A =∫ (x^4/x^5 + 3x^7/x^5 )dx -----> ∫1/x dx + ∫3x^2dx -----> Lnx + 3 * 1/3 x^3 = Lnx + x^3

bounded x=1 to x=2

A = Ln2 +8 - (Ln1 +1) = Ln2 +8 - 0 -1 = Ln2 +7

I hope it is useful,

Minoo