1+ 2x dx - Vidyadip

Question

$\int\sin\text{x}\sqrt{1+\cos2\text{x}}\text{ dx}$

✓

Answer

$\int\sin\text{x}\sqrt{1+\cos2\text{x}}\text{ dx}$
$=\int\sin\text{x}.\sqrt{2\cos^2\text{x}}\text{ dx}$ $[\therefore1+\cos2\text{x}=2\cos^2\text{x}]$
$=\sqrt{2}\int\sin\text{x}\cos\text{x dx}$
$=\frac{\sqrt{2}}{2}\int2\sin\text{x}\cos\text{x dx}$
$=\frac{1}{\sqrt{2}}\int\sin2\text{x dx}$
$=\frac{1}{\sqrt{2}}\Big[\frac{-\cos2\text{x}}{2}\Big]+\text{c}$
$=\frac{-1}{2\sqrt{2}}\cos2\text{x}+\text{c}$

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 Indefinite Integrals→Indefinite Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{y}=\log\sqrt{\tan\text{x}},$ write $\frac{\text{dy}}{\text{dx}}.$

Write the value of $\tan^{-1}\text{x}+\tan^{-1}\Big(\frac{1}{\text{x}}\Big)$ for x > 0.

If f(x) is an even function, then write whether f'(x) is even of odd.

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\log\tan\text{x dx}$

Evaluate the following integrals:
$\int\sin^3\text{x}\cos^6\text{x}\text{ dx}$

Evaluate the following integrals:$\int\frac{\sin2\text{x}}{\sqrt{\cos^4\text{x}-\sin^2\text{x}+2}}\text{ dx}$

Reduce the equation 2x - 3y - 6z = 14 to the normal form and, hence, find the length of the perpendicular from the origin to the plane. Also, find the direction cosines of the normal to the plane.

Find the image of the point (1, 2, 3) in the plane x + 2y + 4z = 38.

Find $|\vec{\text{a}|}$ and $\big|\vec{\text{b}}\big|$ if
$\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=8$ and $|\vec{\text{a}}|=8\big|\vec{\text{b}}\big|$

A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.