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Evaluate: `int (sinx)/(sqrt(36-cos ^(2)x))dx` |
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Answer» We have, `int (sinx)/(sqrt(36-cos^(2)x))dx` Let `cos x=t implies-sin x dx =dt` Putting `sin x dx=-dt and cos x=t.` `=-int (dt)/(sqrt(36-t^(2)))` `=-int(dt)/(sqrt((6)^(2)-t^(2)))` `=-sin^(-1)((t)/(6))+c` `=-sin ^(-1)((cos x)/(6))+c` `[becauset=cosx]` |
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