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If u=inte^(ax)sin " bx dx" and v=inte^...

If `u=inte^(ax)sin " bx dx" and v=inte^(ax)cos " bx dx then "(u^(2)+v^(2))(a^(2)+b^(2))=`

A

`2e^(ax)`

B

`e^(2ax)`

C

`2e^(2ax)`

D

`bxe^(ax)`

Text Solution

Verified by Experts

The correct Answer is:
b
We have , `u=inte^(ax)sin " bx dx" and v=inte^(ax)cos " bx dx"`
`rArru=(e^(ax))/(a^(2)+b^(2))(asin bx - b cos bx)`
and , ` v=(e^(ax))/(a^(2)+b^(2))(a cos bx + b sin bx)`
`:.(u^(2)+v^(2))(a^(2)+b^(2))^(2)=e^(2ax)(a^(2)+b^(2))`
`rArr (u^(2)+v^(2))(a^(2)+b^(2))=e^(2ax)`
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Knowledge Check

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    B
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    C
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