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Evaluate the Integral Help?

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I do not know how to take the antiderivative of fractions, please show steps, thank you! Integral from -2 to 0. (1/8 t^5 + 1/7 t^4 - t) dt
asked May 9, 2013 in CALCULUS by andrew Scholar

1 Answer

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integral subscript minus 2 end subscript superscript 0 open parentheses 1 over 8 t to the power of 5 plus 1 over 7 t to the power of 4 minus t close parentheses d t equal integral subscript minus 2 end subscript superscript 0 open parentheses 1 over 8 t to the power of 5 close parentheses d t plus integral subscript minus 2 end subscript superscript 0 open parentheses 1 over 7 t to the power of 4 close parentheses d t minus integral subscript minus 2 end subscript superscript 0 open parentheses t close parentheses d t    (Integration sum formula)

                                           equal open square brackets 1 over 8 t to the power of 6 over 6 plus 1 over 7 t to the power of 5 over 5 minus t to the power of 2 over 2 close square brackets subscript minus 2 end subscript superscript 0

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equal 0 minus open square brackets 1 over 8 open parentheses minus 2 close parentheses to the power of 6 over 6 plus 1 over 7 open parentheses minus 2 close parentheses to the power of 5 over 5 minus open parentheses minus 2 close parentheses to the power of 2 over 2 close square brackets (Substitute lower limit -2 and upper limit 0)

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equal minus open square brackets 4 over 3 minus 32 over 35 minus 2 close square brackets                                         (Simplify)

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equal open square brackets 166 over 105 close square brackets

 

answered May 11, 2013 by diane Scholar

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