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Calculus question? Please help!?

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Please help with the following question

Find the area between f(x) = x^3 +2 and the x-axis from -1 to 2.
asked Apr 24, 2013 in CALCULUS by linda Scholar
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integral subscript minus 1 end subscript superscript 2 f open parentheses x close parentheses d x space space space space space space space space space space equal integral subscript minus 1 end subscript superscript 2 open parentheses x to the power of 3 plus 2 close parentheses d x

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 integral subscript minus 1 end subscript superscript 0 open parentheses x to the power of 3 plus 2 close parentheses d x plus integral subscript 0 superscript 2 open parentheses x to the power of 3 plus 2 close parentheses d x

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 x to the power of 4 over 4 plus 2 x close square brackets subscript minus 1 end subscript superscript 0 plus open square brackets x to the power of 4 over 4 plus 2 x close square brackets subscript 0 superscript 2            (Apply the upper limits and lower limits)

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 0 to the power of 4 over 4 plus 2 open parentheses 0 close parentheses close square brackets minus open square brackets open parentheses minus 1 close parentheses to the power of 4 over 4 plus 2 open parentheses minus 1 close parentheses close square brackets plus open square brackets 2 to the power of 4 over 4 plus 2 open parentheses 2 close parentheses close square brackets minus open square brackets 0 to the power of 4 over 4 plus 2 open parentheses 0 close parentheses close square brackets    

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 0 close square brackets minus open square brackets 1 over 4 plus 2 open parentheses minus 1 close parentheses close square brackets plus open square brackets 4 plus 4 close square brackets minus open square brackets 0 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 equal minus open square brackets fraction numerator minus 7 over denominator 4 end fraction close square brackets plus open square brackets 8 close square brackets

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 7 over 4 close square brackets plus open square brackets 8 close square brackets

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 39 over 4 close square brackets

The area between the f(x) and x-axis = 39 / 4 sq.units

 

 

 

 

answered May 9, 2013 by diane Scholar

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