Evaluate x x dx - Vidyadip

Question

Evaluate $\int\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$

✓

Answer

Let $\text{I}=\int\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$
Let $\sqrt{\text{x}}=\text{t}$
$\frac{1}{2\sqrt{\text{x}}}\text{dx}=\text{dt}$
$\therefore\ \text{I}=2\int\sin\text{t dt}$
$=-2\cos\text{t}+\text{C}$
$\text{I}=-2\cos\sqrt{\text{x}}+\text{C}$

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

If $I_3$ denotes identity matrix of order $3 \times 3$, write the value of its determinant.

Examine the consistency of the system of equation $2x - y = 5;\,\,x + y = 4$

Write the value of k for which the planes $x - 2y + kz = 4$ and $2x + 5y - z = 9$ are perpendicular.

Let $A=\{3,5,7\}, B=\{2,6,10\}$ and $R$ be a relation from $A$ to $B$ defined by $R=\{(x, y): x$ and $y$ are relatively prime $\}$. Then, write $R$ and $R^{-1}$.

A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that
any two are white?

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$5\frac{\text{d}^2\text{y}}{\text{dx}^2}=\Big\{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big\}^{\frac{3}{2}}$

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as.
$\ \ \ \ \ \ \ \ \ \ \ \ \text{Cost per contact}\\\text{A}=\begin{bmatrix}40&\text{Telephone}\\100&\text{House call}\\50&\text{Letter}\end{bmatrix}$
The number of contacts of each type made in two cities X and Y is given in matrix B as

$\text{BA}=\begin{bmatrix}\text{Telephone}&\text{House call}&\text{Letter}\\1000&500&5000\\3000&1000&10000\end{bmatrix} \begin{matrix}\rightarrow\text{X}\\\rightarrow\text{Y}\end{matrix}$

Find the total amount spent by the group in the two cities X and Y.

Find the area of that parallelogram whose diagonals are denoted by vectors $2 \hat{i}-\hat{j}+5 \hat{k}$ and $3 \hat{i}+\hat{j}+2 \hat{k}$.

Write the value of p for which $\vec{\text{a}}=3\hat{\text{i}}+2\hat{\text{j}}+9\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+\text{p}\hat{\text{j}}+3\hat{\text{k}}$ are parallel vectors.

Evaluate the following:
$\cos^{-1}\Big\{\cos\frac{5\pi}{4}\Big\}$