JEE Main 202125 Feb, Morning shiftMathematicsMediumIntegral Calculus369× since 2002The value of the integral ∫sinθ.sin2θ(sin6θ+sin4θ+sin2θ)2sin4θ+3sin2θ+61−cos2θ dθ\int {{{\sin \theta .\sin 2\theta ({{\sin }^6}\theta + {{\sin }^4}\theta + {{\sin }^2}\theta )\sqrt {2{{\sin }^4}\theta + 3{{\sin }^2}\theta + 6} } \over {1 - \cos 2\theta }}} \,d\theta∫1−cos2θsinθ.sin2θ(sin6θ+sin4θ+sin2θ)2sin4θ+3sin2θ+6dθ is :AOption A. 118[9−2cos6θ−3cos4θ−6cos2θ]32+c{1 \over {18}}{\left[ {9 - 2{{\cos }^6}\theta - 3{{\cos }^4}\theta - 6{{\cos }^2}\theta } \right]^{{3 \over 2}}} + c181[9−2cos6θ−3cos4θ−6cos2θ]23+cBOption B. 118[11−18sin2θ+9sin4θ−2sin6θ]32+c{1 \over {18}}{\left[ {11 - 18{{\sin }^2}\theta + 9{{\sin }^4}\theta - 2{{\sin }^6}\theta } \right]^{{3 \over 2}}} + c181[11−18sin2θ+9sin4θ−2sin6θ]23+cCOption C. 118[11−18cos2θ+9cos4θ−2cos6θ]32+c{1 \over {18}}{\left[ {11 - 18{{\cos }^2}\theta + 9{{\cos }^4}\theta - 2{{\cos }^6}\theta } \right]^{{3 \over 2}}} + c181[11−18cos2θ+9cos4θ−2cos6θ]23+cDOption D. 118[9−2sin6θ−3sin4θ−6sin2θ]32+c{1 \over {18}}{\left[ {9 - 2{{\sin }^6}\theta - 3{{\sin }^4}\theta - 6{{\sin }^2}\theta } \right]^{{3 \over 2}}} + c181[9−2sin6θ−3sin4θ−6sin2θ]23+cCheckSkip · show solution
