int frac{1}{sqrt{x}} sin sqrt{x} , dx = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To solve the integral $\int \frac{1}{\sqrt{x}} \sin \sqrt{x} \, dx$,we use the method of substitution. Let $t = \sqrt{x}$. Then,differentiating bo

Vedclass · Accepted Answer

$-2 \cos \sqrt{x} + c$

Vedclass · Answer

(B) To solve the integral $\int \frac{1}{\sqrt{x}} \sin \sqrt{x} \, dx$,we use the method of substitution. Let $t = \sqrt{x}$. Then,differentiating both sides with respect to $x$,we get $\frac{dt}{dx} = \frac{1}{2\sqrt{x}}$,which implies $\frac{dx}{\sqrt{x}} = 2 \, dt$. Substituting these into the integral,we get: $\int \sin(t) \cdot 2 \, dt = 2 \int \sin(t) \, dt$. The integral of $\sin(t)$ is $-\cos(t)$. Therefore,$2(-\cos(t)) + c = -2 \cos(t) + c$. Substituting back $t = \sqrt{x}$,we get $-2 \cos \sqrt{x} + c$.

$\int \frac{1}{\sqrt{x}} \sin \sqrt{x} \, dx = $

Similar Questions

$\int \frac{x \, dx}{1 - x \cot x} = $

$\int {{e^{ - x}}{{\csc }^2}(2{e^{ - x}} + 5)} \,dx = $

$\int \frac{dx}{x(x^7 + 1)} = $

$\int \frac{\cos x-\sin x}{5+\sin (2 x)} d x=$

Let $f(x) = \frac{x}{(1+x^n)^{1/n}}$ for $n \geq 2$ and $g(x) = \underbrace{(f \circ f \circ \ldots \circ f)}_{n \text{ times }}(x)$. Then $\int x^{n-2} g(x) \, dx$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module