The value of -2-sin x d x-sinx-4

The correct option is C x+log | sin ( x π/4 )+c |√(2)∫sin x dx/sin(x π/4 ) =√(2)∫ sin ( ( x π/4 )+π/4 )/sin ( x π/4 )dx =√(2)∫1/√(2)sin(x π/4)+1/√(2)cos(x ...

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Standard XII

Mathematics

Standard Formulae - 2

The value of ...

Question

The value of $\sqrt{2} \int \frac{s i n x d x}{s i n (x - \frac{π}{4})}$

x + l o g ∣ ∣ c o s (x - \frac{π}{4}) + c ∣ ∣

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x - l o g ∣ ∣ c o s (x - \frac{π}{4}) + x ∣ ∣

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x + l o g ∣ ∣ s i n (x - \frac{π}{4}) + c ∣ ∣

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x - l o g ∣ ∣ c o s (x - \frac{π}{4}) + x ∣ ∣

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Solution

The correct option is C $x + l o g ∣ ∣ s i n (x - \frac{π}{4}) + c ∣ ∣$
$\sqrt{2} \int \frac{s i n x d x}{s i n (x - \frac{π}{4})}$
= $\sqrt{2} \int s i n \frac{((x - \frac{π}{4}) + \frac{π}{4})}{s i n (x - \frac{π}{4})} d x$
= $\sqrt{2} \int \frac{\frac{1}{\sqrt{2}} s i n (x - \frac{π}{4}) + \frac{1}{\sqrt{2}} c o s (x - \frac{π}{4})}{s i n (x - \frac{π}{4})} d x$
= $\int d x + \int c o t (x - \frac{π}{4}) d x = x + \int c o t (x - \frac{π}{4}) d x$
= $x + l o g ∣ ∣ s i n (x - \frac{π}{4}) ∣ ∣ + c$

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Similar questions

Q. The value of

\sqrt{2} \int \frac{sin x d x}{sin (x - \frac{π}{4})}

is
(where

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___

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The value of √2∫sin x dxsin(x−π4)

The correct option is C x+log∣∣sin(x−π4)+c∣∣√2∫sin x dxsin(x−π4) =√2∫sin((x−π4)+π4)sin(x−π4)dx =√2∫1√2sin(x−π4)+1√2cos(x−π4)sin(x−π4)dx =∫dx+∫cot(x−π4)dx=x+∫cot(x−π4)dx =x+log∣∣sin(x−π4)∣∣+c

The value of $\sqrt{2} \int \frac{s i n x d x}{s i n (x - \frac{π}{4})}$