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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{4}{9} $$.x^{3/2}. \sin (x)^{5/2}dx$

$(a)\;\frac{-8}{45} \cos (x^{5/2})+c \qquad(b)\;\frac{-8}{45} \sin (x^{5/2})+c \qquad(c)\;\frac{-8}{9} \cos (x^{5/2})+c \qquad (d)\;\frac{-4}{45} \cos (x^{5/2})+c $
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1 Answer

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$x^{5/2} =t $
differentiate with respect to
$\large\frac{5}{2} x^{3/2} . dx =dt$
=> $x^{3/2} dx=\large\frac{2}{5} $$dt$
=> $\large\frac{4}{9} \int \frac{2}{5} $$ \sin t. dt$
=> $\large\frac{8}{45}$$ \int \sin t. dt$
=> $\large\frac{8}{45}$$ \int \cos t+c$
$\large\frac{-8}{45}$$ \cos (x^{5/2})+c$
Hence a is the correct answer.
answered Dec 24, 2013 by meena.p
 
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