Integrate the function: x x x - Vidyadip

Question

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

✓

Answer

Let $I=\int \frac{\sqrt{\tan x}}{\sin x \cos x}$
$=\int \frac{\sqrt{\tan x} \cdot \cos x}{\sin x \cos x \cdot \cos x} d x$
$= \int \frac{\sqrt{\tan x}}{\tan x \cos ^{2} x} d x$
$= \int \frac{\sec ^{2} x d x}{\sqrt{\tan x}}$
Let $\tan x = t $
$\Rightarrow \sec^2x\ dx = dt$
$\Rightarrow I=\int \frac{d t}{\sqrt{t}}$
$=2 \sqrt{t}+C$
$=2 \sqrt{\tan x}+c$

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 "5 Marks Questions" from Integrals→Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the probability distribution of the number of doublets in three throws of a pair of dice and find its mean.

Evaluate the following intregals:
$\int\frac{\sin2\text{x}}{(1+\sin\text{x})(2+\sin\text{x})}\text{ dx}$

A small firm manufacturers items $A$ and $B$. The total number of items $A$ and $B$ that it can manufacture in a day is at the most $24$. Item A takes one hour to make while item $B$ takes only half an hour. The maximum time available per day is $16$ hours. If the profit on one unit of item $A$ be $Rs. 300$ and one unit of item $B$ be $Rs. 160,$ how many of each type of item be produced to maximize the profit? Solve the problem graphically.

Evaluate the following integrals as limit of sum:
$\int\limits^{5}_{0}(\text{x}+1)\text{dx}$

In order to supplement daily diet, a person wishes to take $X$ and $Y$ tablets. The contents $($in milligrams per tablet$)$ of iron, calcium and vitamins in $X$ and $Y$ are given as below:

Tablets	Iron	Calcium	Vitamin
$X$	$6$	$3$	$2$
$Y$	$2$	$3$	$4$

The person needs to supplement at least $18$ milligrams of iron, $21$ milligrams of calcium and $16$ milligrams of vitamins.
The price of each tablet of $X$ and $Y$ is $₹ 2$ and $₹1$ respectively.
How many tablets of each type should the person take in order to satisfy the above requirement at the minimum cost? Make an $LPP$ and solve graphically.

Find the angle between the lines whose direction cosines are given by the equations: $2l - m + 2n = 0$ and $mn + nl + lm = 0$

Evaluate $\int_{-1}^1 5 x^4 \sqrt{x^5+1} d x$.

Find the matrix A such that
$\begin{bmatrix}1&1\\0&1\end{bmatrix}\text{A}=\begin{bmatrix}3&3&5\\1&0&1\end{bmatrix}$

Evaluate the following integrals:
$\int\frac{\text{x}^2-1}{\text{x}^4+1}\ \text{dx}$

Differentiate the following functions with respect to x:
$\cos^{-1}\big\{2\text{x}\sqrt{1-\text{x}^2}\big\},\frac{1}{\sqrt{2}}<\text{x}<1$