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Question : 73 of 160
Marks:
+1,
-0
Solution:
Given,
∫x2cos2x‌dx=‌f(x)+g(x)sin‌2x+h(x)‌cos‌2‌x+CLHS
I‌=∫x2cos2x‌dx=∫x2(‌)‌dxI‌=‌‌∫(x2+x2‌cos‌2‌x)‌dx‌=‌‌∫x2‌dx+‌‌∫x2‌cos‌2‌x‌dx‌=‌⋅‌+‌I1Where
I1=∫x2cos2x‌dx‌I1=‌sin‌2x+‌x‌cos‌2‌x−‌sin‌2x+C‌⇒I=‌+‌{sin‌2x(‌−‌)+‌‌cos‌2‌x}‌=‌+(‌−‌)sin‌2x+‌‌cos‌2‌x‌=‌f(x)+g(x)sin‌2x+h(x)‌cos‌2‌x+C‌∵f(x)=x3,g(x)=‌−‌‌ and ‌h(x)=‌ ‌⇒f(1)=1,g(2)=‌h(‌)=‌‌∴f(1)+g(2)+h(‌)=1+‌+‌=2
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