Download App

INTEGRALS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINTEGRALS3 Marks
Question
$\int\frac{1+\cos4\text{x}}{\cot\text{x}-\tan\text{x}}\text{dx}$
✓

Answer

$\int\Big(\frac{1+\cos4\text{x}}{\cot\text{x}-\tan\text{x}}\Big)\text{dx}$
$=\int\frac{(1+\cos4\text{x})}{\big(\frac{\cos\text{x}}{\sin\text{x}}-\frac{\sin\text{x}}{\cos\text{x}}\big)}\text{dx}$
$=\int\frac{2\cos^22\text{x}\times\sin\text{x}\cos\text{x}}{(\cos^2\text{x}-\sin^2\text{x})}\text{dx}$
$=\int\frac{\cos^22\text{x}\times2\sin\text{x}\cos\text{x}}{\cos2\text{x}}\text{dx}$
$=\int\cos2\text{x}\sin2\text{x}\text{ dx}$
$=\frac{1}{2}\int2\sin2\text{x}\cos2\text{x dx}$
$=\frac{1}{2}\int\sin4\text{x dx}$
$=\frac{1}{2}\Big[-\frac{\cos4\text{x}}{4}\Big]+\text{c}$
$=-\frac{1}{8}\cos4\text{x}+\text{c}$

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

If $\text{adj A}=\begin{bmatrix} 2 & 3 \\ 4 & -1 \end{bmatrix} \text{and B}=\begin{bmatrix} 1 & -2 \\ -3 & 1 \end{bmatrix},$ find adj AB.
→
If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.
→
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}'(\text{x})=\text{x}^{3}(2\text{x}-1)^{3}$
→
Solve the system of linear equation, using matrix method 2x - y = - 2; 3x + 4y = 3
→
Evaluate the following integrals:
$\int\frac{\text{x}^{\frac{-1}{3}}+\sqrt{\text{x}}+2}{\sqrt[3]{\text{x}}}\text{dx}$
→
Find the second $-$ order derivatives of the function $e^{6x }\cos 3x$
→
Prove that in set $Z$ relation $R$ defined as $a R b$ $\Leftrightarrow a-b$ is divisible by 3 , is equivalence relation.
→
Prove the following:$\cos^{-1}\Bigg(\frac{12}{13}\Bigg)+\sin^{-1}\Bigg(\frac{56}{65}\Bigg)$.
→
Evaluate the following integrals:$\int\text{x}^2\cos\text{x dx}$
→
Evaluate the following integrals:
$\int\text{x}\frac{\tan^{-1}\text{x}^2}{1+\text{x}^4}\text{ dx}$
→