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anonymous
 5 years ago
can someone show me how to find the indefinite integral of 1y^2/3y
anonymous
 5 years ago
can someone show me how to find the indefinite integral of 1y^2/3y

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you mean (1y^2)/3y or 1 (y^2/3y)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok.... first factor out your constant: (1/3) integral (1y^2)/y dy expand the fraction: (1/3) integral (1/y)  y dy now integrate term by term: (1/3) integral (1/y) dy (1/3) integral y dy integral of 1/y is ln(y) and integral of y is ((y^2)/2) solution: (1/3)ln(y)  (y^2)/6 + C

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does that make sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how does 1/3 y dy become y^2/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I factored out the 1/3 first because it's a constant, then integrated y using the power rule, so (Y^2)/2, then multiply by (1/3) which gives (y^2)/6 that you see in the solution.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes! You are great! It made perfect sense, thanks a bunch

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0one more question: Find antiderivative of each derivative that satisfies the given condition: dR/dx = (1x^4)/x^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops left out R(1) = 4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0expand fraction in integrand and seperate: integral 1/x^3 dx  integral x dx evaluate using power rule on each: 1/(2x^2)  ((x^2)/2) + C evaluate using given initial condition of R(1) = 4 and solving for C: R(x) = 1/(2x^2)  ((x^2)/2) + 5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks i understand, but can I express 1/2x^2 instead of factoring out the negative?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops.. my bad.. change 2x to be in denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks a lot... been great help.. is this open 24/7? I might need to come back again later today

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think so, depends on who or how many people are online here i guess...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{4}^{1} (5x+3) dx \] evaluate the integral... I am back already :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops the other way around between 1 and 4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, so...... integral of 5x + 3 = (5/2)x^2 + 3x...now... ((5/2)(4^2) + 3(4))  ((5/2)(1^2) + 3(1)) = 93/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats right.. I left out the 3x.. thanks!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} e^x dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks.. one last question for you

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{1}^{2} (2x^2 3)dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0evaluate the integral

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is that supposed to be 2x^2  3?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no its a negative exponent

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok... so integral of 2x^(2)  3 = (2/x)  3x... then...((2/2)  3(2))  ((2/1)  3(1)) = 7  (5) = 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is where I get confused. since 2/x don't you apply lnx to 1/x?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, the result of integrating 2x^(2) IS 2/x, you don't want to integrate it again, just evaluate it...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that answered my question..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0great.. have a great afternoon and thanks again
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