If we multiply and divide by 8 ,then we have 1/8 times (sin2x) whole cube. Solving it we get the answer -3cos2x/64 +cos6x/192 + c.
Is the method and answer right?

Asked by vaishalikumar68 | 29th Dec, 2015, 10:49: AM

Expert Answer:

Y e s space y o u space a r e space r i g h t. C o n s i d e r space t h e space i n t e g r a l comma space I equals integral sin cubed x cross times cos cubed x space d x equals 8 over 8 integral s i n cubed x cross times c o s cubed x space d x equals 1 over 8 integral 8 s i n cubed x cross times c o s cubed x space d x equals 1 over 8 integral open square brackets 2 sin x cross times cos x close square brackets cubed space d x equals 1 over 8 integral open square brackets sin 2 x close square brackets cubed space d x space space space space space space space space space open square brackets because sin 2 x equals 2 sin x cos x close square brackets equals 1 over 8 integral s i n cubed 2 x d x equals 1 over 8 integral fraction numerator 3 sin 2 x minus sin 6 x over denominator 4 end fraction d x space space space space space space space space space open square brackets because sin 3 A equals 3 sin A minus 4 sin cubed A close square brackets equals 1 over 32 integral open square brackets 3 s i n 2 x minus s i n 6 x close square brackets d x equals 1 over 32 open square brackets integral 3 sin 2 x d x minus integral sin 6 x d x close square brackets equals 3 over 32 integral s i n 2 x d x minus 1 over 32 integral s i n 6 x d x equals 3 over 32 open parentheses fraction numerator negative cos 2 x over denominator 2 end fraction close parentheses minus 1 over 32 open parentheses fraction numerator negative c o s 6 x over denominator 6 end fraction close parentheses plus C equals fraction numerator negative 3 c o s 2 x over denominator 64 end fraction plus fraction numerator c o s 6 x over denominator 192 end fraction plus C

Answered by Vimala Ramamurthy | 29th Dec, 2015, 11:18: AM