Evaluate: dx 5-4x - 2x^ 2 . - Vidyadip

Question

Evaluate: $\int\frac{\text{dx}}{\sqrt{5-4\text{x - 2x}^{2}}}.$

✓

Answer

$\int\frac{\text{dx}}{\sqrt{5-4\text{x}-\text{2x}^{2}}}=\frac{1}{\sqrt{2}}\int\frac{\text{dx}}{\sqrt{\frac{5}{2}-\text{2x - x}^{2}}}=\frac{1}{\sqrt{2}}\int\frac{\text{dx}}{\sqrt{\Bigg(\sqrt\frac{7}{2}\Bigg)^{2}-(\text{x + 1})^{2}}}$
$=\frac{1}{\sqrt{2}}\cdot\sin^{-1}\Bigg(\frac{\text{x + 1}}{\frac{\sqrt{7}}{\sqrt{2}}}\Bigg)+\text{c}$
$\text{Or}\frac{1}{\sqrt{2}}\sin^{-1}\Bigg(\frac{\sqrt{2}}{7}\cdot\text{(x + 1)}\Bigg)+\text{c}.$

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 "5 Marks Questions" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A bag contains 25 tickets, numbered from 1 to 25. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.

Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}} = (\text{x}+\text{y})^2$

If $\text{x}=\text{e}^{\cos2\text{t}}$ and $\text{y}=\text{e}^{\sin2\text{t}},$ prove that $\frac{\text{dy}}{\text{dx}}=-\frac{\text{y}\log\text{x}}{\text{x}\log\text{y}}$

Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

Evaluate the following integrals:
$\int\frac{\text{e}^{\text{x}}}{\text{x}}\Big\{\text{x}(\log\text{x})^2+2\log\text{x}\Big\}\text{dx}$

Find the angle of intersecting of the following curves:
$\text{y}^2=\text{x}\text{ and }\text{x}^2=\text{y}$

Consider a non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then, R is:

Symmetric but not transitive.
Transitive but not symmetric.
Neither symmetric nor transitive.
Both symmetric and transitive.

Evaluate the following integrals:
$\int\frac{\text{x}^2}{(\text{x}^2+1)(3\text{x}^2+4)}\ \text{dx}$

A and B toss a coin alternately till one of them gets a head and wins the game. If A starts the game, find the probability that B will win the game.

Find values of k, if area of triangle is $4$ square units whose vertices are:
$(-2, 0), (0, 4), (0, k)$