Evalute the following integrals: 2x dx - Vidyadip

Question

Evalute the following integrals:
$\int\frac{\sec\text{x}}{\sec2\text{x}}\text{dx}$

✓

Answer

Let $\text{I}=\int\frac{\sec\text{x}}{\sec2\text{x}}\text{dx},$ then
$\text{I}=\int\frac{\frac{1}{\cos\text{x}}}{\frac{1}{\cos2\text{x}}}\text{dx}$
$=\int\frac{\cos2\text{x}}{\cos\text{x}}\text{dx}$
$=\int\frac{2\cos^2\text{x}-1}{\cos\text{x}}\text{dx}$
$=\int2\cos\text{ x dx}-\int\frac{1}{\cos\text{x}}\text{dx}$
$=2\int\cos\text{dx}-\int\sec\text{x dx}$
$=2\sin\text{x}-\log|\sec\text{x}+\tan\text{x}|+\text{C}$
$\because\text{I}=2\sin\text{x}-\log|\sec\text{x}+\tan\text{x}|+\text{C}$

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 "Solve the Following Question.(3 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $y =\log _{ e } x$, then find $\Delta y$ when $x =3$ and $\Delta x =0.03$

Find the principal value of the following:
$\sec^{-1}\Big(2\sin\frac{3\pi}{4}\Big)$

Evaluate the following:

If $\int_a^a \sqrt{x} d x=2 a \int_0^{\pi / 2} \sin ^3 x d x$, find the value of $\int_a^{a+1} x d x$.

Find the approximate change in the value V of a cube of side x metres caused by increasing the side by $1\%.$

Find the mean and standard deviation of the following probability distributions:

$x_i$	-1	0	1	2	3
$p_i$	0.3	0.1	0.1	0.3	0.2

A water tank in the form of an inverted cone is being emptied at the rate of 2 cubic feet per second. The height of the cone is 8 feet and the radius is 4 feet. Find the rate of change of the water level when the depth is 6 feet.

Prove by vector method, that the angle subtended on semicircle is a right angle.

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three unit vectors such that $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{c}},\vec{\text{b}}\times\vec{\text{c}}=\vec{\text{a}},\vec{\text{c}}\times\vec{\text{a}}=\vec{\text{b}}.$Show that $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ from an orthonormal right handed triad of unit vectors.

A wire of length 36 meters is bent to form a rectangle. Find its dimensions if the area of the rectangle is maximum.

Find the area of the triangle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).