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Question : 73 of 160
Marks:
+1,
-0
Solution:
∫e4x(sin‌3x−cos‌3‌x)‌dx=∫e4xsin‌3x‌dx−∫e4x‌cos‌3‌x‌dxUsing the standard integrals
‌∫eaxsin‌bx‌dx=‌(asin‌bx−b‌cos‌b‌x)‌∫eax‌cos‌b‌x‌dx=‌(a‌cos‌b‌x+bsin‌bx)Here,
a=4,b=3So,
∫e4x(sin‌3x−cos‌3‌x)‌dx‌=‌(4sin‌3x−3‌cos‌3‌x)−‌(4‌cos‌3‌x+3sin‌3x)+C⇒‌[4sin‌3x−3‌cos‌3‌x−4‌cos‌3‌x−3sin‌3x]+C⇒‌[sin‌3x−7‌cos‌3‌x]+C
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