Download App

Indefinite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIndefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\Big\{3\sin\text{x}-4\cos\text{x}+\frac{5}{\cos^2\text{x}}-\frac{6}{\sin^2\text{x}}+\tan^2\text{x}-\cot^2\text{x}\Big\}\text{dx}$
✓

Answer

$\int\Big\{3\sin\text{x}-4\cos\text{x}+\frac{5}{\cos^2\text{x}}-\frac{6}{\sin^2\text{x}}+\tan^2\text{x}-\cot^2\text{x}\Big\}\text{dx}$
$=3\int\sin\text{x dx}-4\int\cos\text{x dx}+5\int\sec^2\text{dx}\\-6\int\text{cosec}^2\text{x}+\int\tan^2\text{x dx}-\int\cot^2\text{x dx}$
$=3\int\sin\text{x dx}-4\int\cos\text{x dx}+5\int\sec^2\text{x dx}\\-6\int\text{cosec}^2\text{x}+\int(\sec^2\text{x}-1)\text{dx}-\int(\text{cosec}^2\text{x}-1)\text{dx}$
$=3\int\sin\text{x dx}-4\int\cos\text{x dx}+6\int\sec^2\text{x dx}-7\int\text{cosec}^2\text{x dx}$
$=-3\cos\text{x}-4\sin\text{x}+6\tan\text{x}+7\cot\text{x}+\text{C}$

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 "2 Marks Questions" 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

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{9\pi}{5}\Big)$
→
If $A = \{1, 2, 3\}$ and $B = \{a, b\},$ write the total number of functions from $A$ to $B$.
→
A bag contains $4$ red and $4$ black balls, another bag contains $2$ red and $6$ black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
→
If $\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y} \end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6 \end{bmatrix},$ write the value of (x + y + z).
→
For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if 
$\vec{\text{a}}=\lambda\hat{\text{i}}+2\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=5\hat{\text{i}}-9\hat{\text{j}}+2\hat{\text{k}}$
→
Find x, y satisfying the matrix equation.
$\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0$
→
If $f : C \rightarrow C$ is defined by $f(x) = x^4,$ write $f^{-1}(1).$
→
Show that the following systems of linear equations has infinite number of solutions and solve:
x + 2y = 5,
3x + 6y = 15
→
Find the value of $\int \operatorname{cosec}^2 x \sec ^2 x \ d x$.
→
Evaluate the following integrals:
$\int\limits^2_02\text{x}\big[\text{x}\big]\text{dx}$
→