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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Intergate : $\int \large\frac{5}{7} $$ \sqrt {\cos (7x)}. \sin 7x dx$

$(a)\;(\tan 7x)^{3/2}+c \qquad(b)\;(\cot 7x)^{3/2}+c \qquad(c)\;\frac{-10}{147} [(\cos 7x)^{3/2}]+c\qquad (d)\;(\sin 7x )^{3/2} +c $

1 Answer

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$\cos 7x =t$
differentiate with x
$-\sin 7(x) dx=dt$
=> $\sin 7x dx= -\large\frac{dt}{7}$
=> $- \int \large\frac{5}{49}$$ \sqrt t .dt$
=> $\large\frac{-5}{49} [t^{3/2}] \times \large\frac{2}{3} $$+c$
$\large\frac{-10}{147}$$ [(\cos 7x)^{3/2}]+c$
Hence c is the correct answer.
answered Dec 24, 2013 by meena.p