Solve
∫ lower limit 01. upper limit 2. x^(5) - x^(-1) / x^2 ; dx
The answer is 27/8 but how did they get that?
∫ lower limit 01. upper limit 2. x^(5) - x^(-1) / x^2 ; dx
The answer is 27/8 but how did they get that?
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Ok, to take the integral the easiest thing first is to simplify your problem
(x^5 - x^-1)/x^2
x^5/x^2 - x^-1/x^2
x^3 - x^-3
From here integration is a snap, using basic rules that integral of x^a = (x^(a + 1))/(a + 1)
The integral of our problem is
(x^4)/4 - (x^-2)/(-2)
x^4/4 + x^-2/2
You should be able to get to the answer from there
(x^5 - x^-1)/x^2
x^5/x^2 - x^-1/x^2
x^3 - x^-3
From here integration is a snap, using basic rules that integral of x^a = (x^(a + 1))/(a + 1)
The integral of our problem is
(x^4)/4 - (x^-2)/(-2)
x^4/4 + x^-2/2
You should be able to get to the answer from there
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http://www4d.wolframalpha.com/Calculate/…