Practicing Success
Practicing Success
CUET Preparation Today
$\int \frac{\sin x-\cos x}{\sqrt{1-\sin 2 x}} e^{\sin x} \cos x d x$ is equal to |
$e^{\sin x}+c$ $e^{\sin x-\cos x}+c$ $e^{\sin x+\cos x}+c$ $e^{\cos x-\sin x}+c$ |
$e^{\sin x}+c$ |
$I=\int e^{\sin x} \cos x d x=e^{\sin x}$ as $1-\sin 2 x=(\sin x-\cos x)^2$ Hence $\int e^{\sin x} \cos x d x$ Put $\sin x=t \Rightarrow \cos x d x=d t$ $\int e^t d t=e^t+c=e^{\sin x}+c$ Hence (1) is the correct answer. |
