First slide

Methods of integration

Question

If $\int (\sin 2 x - \cos 2 x) d x = \frac{1}{\sqrt{2}} \sin (2 x + k) + C$
then

Easy

A

$k = π / 4$
B

$k = 5 π / 4$
C

$k = 3 π / 4$
D

none of these

Solution

Write the given integral as $- \sqrt{2} \int \cos (2 x + x / 4) d x$
$= - \frac{1}{\sqrt{2}} \sin (2 x + \frac{π}{4}) + C = \frac{1}{\sqrt{2}} \sin (2 x + \frac{5 π}{4}) + C .$

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