Download App

Indefinite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIndefinite Integrals2 Marks
Question
Evaluate the following intregals:
$\int\frac{\text{x}-1}{\sqrt{\text{x}^2+1}}\text{dx}$
✓

Answer

$\int\frac{\text{x}-1}{\sqrt{\text{x}^2+1}}\text{dx}$
$=\int\frac{\text{x}}{\sqrt{\text{x}^2+1}}-\frac{1}{\sqrt{\text{x}^2+1}}\text{dx}=\frac{1}{2}\int\frac{2\text{x}}{\sqrt{\text{x}^2+1}}\text{dx}-\int\frac{1}{\sqrt{\text{x}^2+1}}\text{dx}$
$=\frac{1}{2}\int\frac{\text{dt}}{\sqrt{\text{t}}}-\int\frac{1}{\sqrt{\text{x}^2+1}}\text{dx}=\frac{1}{2}(2\sqrt{\text{t}})-\int\frac{1}{\sqrt{\text{x}^2+1}}\text{dx}\\=\sqrt{\text{t}}-\text{In}\big|\text{x}+\sqrt{\text{x}^2+1}\big|+\text{c}$
$=\sqrt{\text{x}^2+1}-\text{In}\big|\text{x}+\sqrt{\text{x}^2+1}\big|+\text{c}$

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

Find the general solution of the differential equation $\frac{d y}{d x}+\sqrt{\frac{1-y^{2}}{1-x^{2}}}=0$
→
Verify that $A^2 = I,$ when $\text{A}=\begin{bmatrix}0&1&-1\\4&-3&4\\3&-3&4\end{bmatrix}.$
→
If $R = \{(x, y): x^2 + y^2 \leq 4; x, y \in Z\}$ is a relation on $Z,$ write the domain of $R.$
→
Evaluate the following intregals:
$\int\frac{6\text{x}-5}{\sqrt{3\text{x}^2-5\text{x}+1}}\text{ dx}$
→
Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by $:\text{a}_\text{ij}=\frac{(\text{i}+\text{j})^2}{2}$
→
Evaluate the following:
$\cos\Big(\tan^{-1}\frac{24}{7}\Big)$
→
Evaluate the following:
$\sin\Big(\tan^{-1}\frac{24}{7}\Big)$
→
State whether the function is one-one, onto or bijective. Justify your answer. $f: R \rightarrow R$ defined by $f(x) = 3 - 4x.$
→
If $\text{A}=\begin{bmatrix}2 & 3 \\4 & 5 \end{bmatrix},$ prove that $A - A^T$ is a skew symmetric matrix.
→
Evaluate the following integrals:
$\int\frac{1}{1-\cos2\text{x}}\text{dx}$
→