Evaluate the following integrals: ^2x 4+ ^2x dx - Vidyadip

Question

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

✓

Answer

Let $\tan\text{x}=\text{t}$ $\Rightarrow\sec^2\text{x}\text{ dx}=\text{dt}$ $\Rightarrow\int\frac{\sec^2\text{x}}{\sqrt{\tan^2\text{x}+4}}\text{ dx}=\int\frac{\text{dt}}{\sqrt{\text{t}^2+2^2}}$$=\log\Big|\text{t}+\sqrt{\text{t}^2+4}\Big|+\text{C}$
$=\log\Big|\tan+\sqrt{\tan^2\text{x}+4}\Big|+\text{C}$

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 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

Find $\frac{d y}{d x}$ if $ax + by^2 = \cos y$

Find the volume of the parallelopiped with its edges represented by the vectors
$\hat{\text{i}}+\hat{\text{j}},\hat{\text{i}}+2\hat{\text{j}}$ and $\hat{\text{i}}+\hat{\text{j}}+\pi{\text{k}}.$

Find the equation of the plane passing through the following point:
(1, 1, 1), (1, -1, 2) and (-2, -2, 2)

Find the angle between the vectors $\vec{\text{a}} $ and $\vec{\text{b}},$ where$\vec{\text{a}}=2\hat {\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}} =4\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}}$

A random variable X has the following probability distribution:

Values of X:	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Determine:
The Value of a.

For the following differntial equations verify that the accompanying function is a solution:

Differential equation	Function
$\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$	$\text{y}=\text{ax}$

If f(x) = x + 1 then write the value of $\frac{\text{d}}{\text{dx}}\text{ fof }\text{(x)}.$

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x], where [x] denotes the greatest integer less than or equal to x.

If y = x|x|, find $\frac{\text{dy}}{\text{dx}}\text{ for x 0}<0.$

$\int\tan^2(2\text{x}-3)\text{dx}$