Integrate the function: x x - Vidyadip

Question

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

✓

Answer

Let $I = \int {\frac{{\cos \sqrt x }}{{\sqrt x }}dx} $ ...(i)Putting $\sqrt x = t$
$\Rightarrow x = t^2$
$ \Rightarrow \frac{{dx}}{{dt}} = 2t$
$ \Rightarrow $ dx = 2tdt
$\therefore$ From eq. (i), $I = \int {\frac{{\cos t}}{t}2tdt} $
$ = 2\int {\cos t\,dt} $
= 2 sin t + c
$ = 2\sin \sqrt x + c$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write $A^{-1}$ for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$

X is taking up subjects - Mathematics, Physics and Chemistry in the examination. His probabilities of getting grade A in these subjects are 0.2, 0.3 and 0.5 respectively. Find the probability that he gets,
Grade A in no subject.

Find area of the triangle with vertices at the point given (1, 0), (6, 0), (4, 3).

Let * be a binary operation on Q - {-1} defined by a * b = a + b + ab for all a, b ∈ Q - {-1}. Then,
Find the identity element in Q − {−1}.

Reflexive and transitive but not symmetric.

Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=8$

If $\text{A}=\begin{bmatrix}\cos\text{a}&-\sin\text{a}\\\sin\text{a}&\cos\text{a} \end{bmatrix}$ is identity matrix, then write the value of a.

Write a value of $\int\sqrt{\text{x}^2-9}\text{ dx}$

Write the vector equation of a line passing through a point having position vector $\vec{\alpha}$ and parallel to vector $\vec{\beta}.$

Let $\text{f}:\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big)\rightarrow\ \text{R}$ be a function defined by f(x) = cos[x]. write range (f).