CUET Preparation Today
Find: $\int \cos^3 x e^{\ln \sin x} dx$ |
$\frac{\cos^4 x}{4} + C$ $-\frac{\sin^4 x}{4} + C$ $-\frac{\cos^4 x}{4} + C$ $\frac{\sin^4 x}{4} + C$ |
$-\frac{\cos^4 x}{4} + C$ |
The correct answer is Option (3) → $-\frac{\cos^4 x}{4} + C$ Let, $I = \int \cos^3 x e^{\ln \sin x} dx$ Or, $I = \int \cos^3 x \sin x dx$ Put, $\cos x = t ⇒-\sin x dx = dt$ $∴I = -\int t^3 dt$ Or, $I = -\frac{t^4}{4} + C$ Or, $I = -\frac{\cos^4 x}{4} + C$ |
