Evaluate int sqrt(1 + sin 2 x ) " dx " (...

Evaluate `int sqrt(1 + sin 2 x ) " dx " (x in" R")`.

Text Solution

Verified by Experts

The correct Answer is:

`{(sinx +cosx +c " if " x in [2 n pi -(pi)/(4)","2npi +(3pi)/(4)]),(cosx-sinx+c" if "x in[2npi+(3pi)/(4)","2npi+(7pi)/(4)]","n inZ):}`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INDEFINITE INTEGRALS
AAKASH SERIES|Exercise ADDITIONAL SOLVED EXAMPLES|3 Videos
INDEFINITE INTEGRALS
AAKASH SERIES|Exercise EXERCISE - 1.1(VERY SHORT ANSWER QUESTIONS)|45 Videos
HYPERBOLA
AAKASH SERIES|Exercise Exercise|6 Videos
LOGARITHMIC SERIES
AAKASH SERIES|Exercise EXERCISE - III|8 Videos

AAKASH SERIES-INDEFINITE INTEGRALS -PRACTICE EXERCISE

Evaluate int sqrt(1 + sin 2 x ) " dx " (x in" R").
Text Solution
|
If f(x), g(x) are primitives of phi (x) then
Text Solution
|
int (1-x^(4))/(1-x)dx=
Text Solution
|
int (x^(4) + x^(2) +1)/(x^(2) + 1) dx =
Text Solution
|
int (x^(6) - 1)/(x^(2) +1) dx =
Text Solution
|
int (x^(8))/(x^(6) + 1) dx =
Text Solution
|
int sin^(2)x sec^(2) x dx=
Text Solution
|
int (tan x - cot x )^(2) dx =
Text Solution
|
int(1)/(1+ cos x) dx on I sub R \\{(2n +1) pi : n in Z}.
Text Solution
|
int (1)/(1 + cos 2 x) dx =
Text Solution
|
int (1)/(cos 2 x + sin^(2) x) dx =
Text Solution
|
If 0 lt x lt (pi)/(2) then int [ 1+ 2 cot x (cot x " cosecx" )]^(1//...
Text Solution
|
Evaluate int ("cos" 2x - cos 2 alpha)/(cos x - cos alpha )
Text Solution
|
If x in ((pi)/(6), (pi)/(3)) " then " int tan^(-1) sqrt((1 - cos 2x)/(...
Text Solution
|
int (sin (x -a))/(sin x) dx =
Text Solution
|
int (sin(x-a))/(cos (x-b))dx=
Text Solution
|
If int (sin 2x + cos 2x) dx = (1)/(sqrt(2)) sin (2x - c) + a then c =
Text Solution
|
int sin^(3) x.cos^(2) x dx =
Text Solution
|
int (sin x cos x)/(1 + cos^(4) x ) dx =
Text Solution
|
int (cos x + x sin x)/(x (x - cos x)) dx=
Text Solution
|
int (1)/((e^(x) - e^(-x))^(2)) dx =
Text Solution
|