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Question : 72 of 160
Marks:
+1,
-0
Solution:
Let
I=∫x3sin‌3x‌dxI‌=x3‌∫sin‌3x‌dx−∫(‌(x3)‌∫sin‌3x‌dx)‌dx‌=‌−∫‌| 3x2×(−cos‌3‌x)‌dx |
| 3 |
‌=‌+∫x2‌cos‌3‌x‌dx+c1Let
I1=∫x2‌cos‌3‌x‌dx‌I1=x2‌∫cos‌3‌x‌dx−∫(‌(x2)‌∫cos‌3‌x‌dx)‌dx‌I1=‌−∫‌‌dx+c2‌‌ Let ‌I3=∫xsin‌3x‌dx‌⇒I3=x‌∫sin‌3x‌dx−∫(‌(x)‌∫sin‌3x‌dx)‌dx‌⇒I3=‌−∫‌‌dx‌⇒I3=‌+‌+c3So,
I=‌+‌−‌(‌+‌)+C ‌⇒I=‌[−9x3‌cos‌3‌x+9x2sin‌3x+6x‌cos‌3‌x−2sin‌3x]+C‌⇒‌‌f(x)=6x−9x3‌‌‌g(x)=9x2−2‌⇒‌‌f(1)=−3,‌‌g(1)=7‌⇒f(1)+g(1)=4
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