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 Question" 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

A box has $5$ blue and $4$ red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?

Find the binomial distribution for which the mean is 4 and variance 3.

Let $\text{F}(\alpha)=\begin{bmatrix}\cos\alpha & -\sin\alpha & 0 \\ \sin\alpha & \cos\alpha & 0 \\ 0 & 0 & 1\end{bmatrix}$ and
$\text{G}(\beta)=\begin{bmatrix} \cos\beta & 0 & \sin\beta \\ 0 & 1 & 0 \\ -\sin\beta & 0 & \cos\beta \end{bmatrix}$
Show that
$\big[\text{G}(\beta)\big]^{-1}=\text{G}(-\beta)$

The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.

A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?

Differentiate the following functions with respect to x:
$\sin(\log\text{x})$

If $A = [a_{ij}]$ is a skew-symmetric matrix, then write the value of $\sum_\text{i}\text{a}_\text{ij}.$

Evaluate the following integrals:
$\int\text{e}^{\text{x}}(\cos\text{x}-\sin\text{x})\text{dx}$

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a * b =min. {a, b}. Write the operation table of the operation *.