Evaluate the following: + 1+ 2x dx - Vidyadip

Question

Evaluate the following:
$\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1+\sin2\text{x}}}\text{dx}$

✓

Answer

Let $\text{I}=\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1+\sin2\text{x}}}\text{dx}$ $=\int\frac{(\sin\text{x}+\cos\text{x})}{\sqrt{\sin^2\text{x}+\cos^2\text{x}+2\sin\text{x}\cos\text{x}}}\text{dx}$
$=\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{(\sin\text{x}+\cos\text{x})^2}}\text{dx}$ $=\int1\text{dx}=\text{x}+\text{C}$

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 "3 Marks" 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

Represent the followinf families of curves by forming the corresponding differential equation:
$\text{y}=\text{e}^{\text{ax}}$

With reference to the right handed system of mutually perpendicular unit vectors
$\hat{i}, \hat{j}$ and $\hat{k}$, if $\vec{\alpha}=3 \hat{i}-\hat{j}, \vec{\beta}=2 \hat{i}+\hat{j}-3 \hat{k}$, then express $\vec{\beta}$ in the form $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, where $\vec{\beta}_1$ is parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ is perpendicular to $\vec{\alpha}$.

Find the integrals of the functions in Exercises:
$\sin^3\text{x}\cos^3\text{x}$

Find the slopes of the tangent and the normal to the following curves at the indicated points:
$\text{x}=\text{a}(\theta-\sin\theta),\text{y}=\text{a}(1-\cos\theta)\text{at}\ \theta=\frac{\pi}{2}$

Evaluate the following integrals:
$\int\text{x}^2\text{e}^{\text{x}^3}\cos\big(\text{e}^{\text{x}^3}\big)\text{dx}$

If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
$\text{B}+\text{C}-2\text{A}$

Find the general solution of $\frac{d y}{d x}+3 y=e^{-2 x}$

Solve the following equation for x:
$\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big)+\cot^{-1}\Big(\frac{1-\text{x}^2}{2\text{x}}\Big)=\frac{2\pi}{3},\text{x}>0$

How many times must a man toss a fair coin so that the probability of having at least one head is more than 80%?

Evaluate the following integrals:
$\int\limits^1_{-1}\text{x|x|}\text{dx}$