If ∫( sin 4 x- cos 4 x) d x=-( sin 2 x/k)+c then find k

Question

If ∫( sin 4 x- cos 4 x) d x=-( sin 2 x/k)+c then find k (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

∫( sin 4 x- cos 4 x) d x =∫( sin 2 x- cos 2 x)( sin 2 x+ cos 2 x) d x =∫( sin 2 x- cos 2 x) d x =-∫( cos 2 x- sin 2 x) d x=-∫ cos 2 x d x =(- sin 2 x/2)+c

Q. If $\int (sin^{4} x - cos^{4} x) d x = - \frac{s i n 2 x}{k} + c$ then find $k$

$\int (sin^{4} x - cos^{4} x) d x$
$= \int (sin^{2} x - cos^{2} x) (sin^{2} x + cos^{2} x) d x$
$= \int (sin^{2} x - cos^{2} x) d x$
$= - \int (cos^{2} x - sin^{2} x) d x = - \int cos 2 x d x$
$= \frac{- s i n 2 x}{2} + c$

Q. If ∫(sin4x−cos4x)dx=−ksin2x​+c then find k

∫(sin4x−cos4x)dx =∫(sin2x−cos2x)(sin2x+cos2x)dx =∫(sin2x−cos2x)dx =−∫(cos2x−sin2x)dx=−∫cos2xdx =2−sin2x​+c

Q. If $\int (sin^{4} x - cos^{4} x) d x = - \frac{s i n 2 x}{k} + c$ then find $k$

$\int (sin^{4} x - cos^{4} x) d x$
$= \int (sin^{2} x - cos^{2} x) (sin^{2} x + cos^{2} x) d x$
$= \int (sin^{2} x - cos^{2} x) d x$
$= - \int (cos^{2} x - sin^{2} x) d x = - \int cos 2 x d x$
$= \frac{- s i n 2 x}{2} + c$