Integrate the function frac{cos sqrt{x}}{sqrt | vedclass

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Question

(A) Let $\sqrt{x} = t$. Then,differentiating both sides with respect to $x$,we get $\frac{1}{2\sqrt{x}} dx = dt$,which implies $\frac{1}{\sqrt{x}} dx

Vedclass · Accepted Answer

$2 \sin \sqrt{x} + C$

Vedclass · Answer

(A) Let $\sqrt{x} = t$. Then,differentiating both sides with respect to $x$,we get $\frac{1}{2\sqrt{x}} dx = dt$,which implies $\frac{1}{\sqrt{x}} dx = 2 dt$. Substituting these into the integral: $\int \frac{\cos \sqrt{x}}{\sqrt{x}} dx = \int \cos(t) \cdot (2 dt) = 2 \int \cos(t) dt$. Integrating $\cos(t)$ gives $\sin(t)$,so we have $2 \sin(t) + C$. Substituting back $t = \sqrt{x}$,the final result is $2 \sin \sqrt{x} + C$,where $C$ is an arbitrary constant.

Integrate the function $\frac{\cos \sqrt{x}}{\sqrt{x}}$.

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