Find: dx 3 - 2x - x^ 2 - Vidyadip

Question

Find:
$\int \frac{\text{dx}}{\sqrt{3 - \text{2x - x}^{2}}}$

✓

Answer

$\text{I} = \int \frac{\text{dx}}{\sqrt{(2)^{2} - \text{(x + 1)}^{2}}}$
$= \sin^{-1} \bigg(\frac{\text{x + 1}}{2}\bigg) + \text{c}$

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 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

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ find $\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{a}}\big).$

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line $\text{5x – 25 = 14 – 7y = 35z.}$

Find the value of $\sin \left[2 \sin ^{-1}(0.6)\right]$

Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.

Construct a 3$\times$4 matrix, whose elements are given by aij $ = \frac{1}{2}\left| { - 3i + j} \right|$

Evaluate the following integrals:$\int\frac{\sec^2\text{x}}{\sqrt{4+\tan^2\text{x}}}\text{ dx}$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are position vectors of the points A, B and C respectively, write the value of$\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}+\overrightarrow{\text{AC}}$.

Find the value of $\int \operatorname{cosec}^2 x \sec ^2 x \ d x$.

Find the second order derivatives of the function given in Exercise:
$\sin(\log\text{x})$

Examine the continuity of the function $f(x) = 2x^2 – 1$ at $x = 3.$