The correct option is C I= 4cosπ4xπ+C ∫sinπ x4 dx Putting π x4 = m π dx4 = dm ∫4πsin m dm = 4 cosπ x4π+C ...

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Sum of Trigonometric Ratios in Terms of Their Product

Solve ∫sinπ...

Question

Solve $\int sin (\frac{π}{4} x) d x$ .

I = \frac{cos \frac{π}{4} x}{π} + C

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I = \frac{4 cos \frac{π}{4} x}{π} + C

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I = \frac{- 4 cos \frac{π}{4} x}{π} + C

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Solution

The correct option is C $I = \frac{- 4 cos \frac{π}{4} x}{π} + C$
$\int sin \frac{π x}{4} d x$
Putting $\frac{π x}{4} = m$
$\frac{π d x}{4} = d m$
$\int \frac{4}{π} sin m d m$
$= \frac{- 4 cos \frac{π x}{4}}{π} + C$

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