document.write( "Question 1123840: if u= int (f(sin2x)sinx)dx on [0 ,pi/2] and v= int (f(cos2x)cosx)dx on [0 ,pi/2]
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Algebra.Com's Answer #740214 by ikleyn(52865) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "    if u= int (f(sin^2(x))sinx)dx on [0 ,pi/2] and v= int (f(cos^2(x))cosx)dx on [0 ,pi/2]\r\n" );
document.write( " then u/v =......\r\n" );
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document.write( "Use the change of variables\r\n" );
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document.write( "    u = int (f(sin^2(x))sinx)dx on [0 ,pi/2] = int (-f(sin^2(x))d(cos(x)) on [0 ,pi/2] = int (-f(1-cos^2(x))d(cos(x)) on [0 ,pi/2] =\r\n" );
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document.write( "      = -int (f(1-t^2)dt  on [1,0]  (where t = cos(x) );\r\n" );
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document.write( "    v = int (f(cos^2(x))cosx)dx [0 ,pi/2] = int (f(cos^2(x))d(sin(x))dx [0 ,pi/2] = int (f(1-sin^2(x))d(sin(x))dx [0 ,pi/2] = \r\n" );
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document.write( "      = int (f(1-t^2)dt on [0,1]  (where t = sin(x) ).\r\n" );
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document.write( "   Since  -int (f(1-t^2)dt  on [1,0] = int (f(1-t^2)dt on [0,1],  we have   = 1.\r\n" );
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