If intsqrt(1+sec x) dx = K sin^(-1)(f(x)...

If `intsqrt(1+sec x) dx = K sin^(-1)(f(x)) + C` then

A

`f(x) = sqrt(2)sin (x//2)`

B

`f(x) = sqrt(2) cos (x//2), K = 2`

C

`f(x) = sqrt(2) tan (x//2), K = 2`

D

`f(x) = sqrt(2) sin (x//2), K = sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:

A

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INDEFINITE INTEGRATION
MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLE ( LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTION ))|23 Videos
INDEFINITE INTEGRATION
MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLE ( NUMERICAL ANSWER TYPE QUESTION )|16 Videos
INDEFINITE INTEGRATION
MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B - ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos
HYPERBOLA
MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|8 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS |3 Videos

Similar Questions

Explore conceptually related problems

intsqrt(1+sin 2x) dx

intsqrt(1+cos 2x) dx

intsqrt(1-cos 2x) dx

If int sqrt(1+sec x)dx=2sin^(-1)[sqrt(2)f(x)]+c then (d)/(dx)[f(x)] is equal to (A)cos(x)/(2)(B)-(1)/(2)cos(x)/(2)(C)(1)/(2)cos(x)/(2)(D)(1)/(2)sin(x)/(2)

intsqrt(1+sin2x)dx=

intsqrt(1-sin7x)dx=

intsqrt(1+cos5x)dx=

intsqrt (1+cos2x)dx

If int (2^(x))/(sqrt(1-4^(x))) dx = k sin ^(-1) (f(x)) + C then :

MCGROW HILL PUBLICATION-INDEFINITE INTEGRATION-SOLVED EXAMPLE ( LEVEL 1 ( SINGLE CORRECT ANSWER TYPE QUESTION ))

If int (cos4x+1)/(cot x - tanx)=Kcos4x+C, then
Text Solution
|
inte^(x)(1+sinx)/(1+cosx)dx is equal to
Text Solution
|
If intsqrt(1+sec x) dx = K sin^(-1)(f(x)) + C then
Text Solution
|
The antiderivative of f (x) = log (log x ) + 1/(log x)^(2) whose graph...
Text Solution
|
int(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)(a,bgt0) is equal to
Text Solution
|
f(x) = (1//2) (x^(2) - 1)
Text Solution
|
The function f whose graph passes through (0,7/3) and whose derivative...
Text Solution
|
The value of int (sin alpha)/(sqrt(1+cos alpha)) dalpha is
Text Solution
|
The value of int(dx)/(5+4cosx) is
Text Solution
|
int(dx)/(x(x^(4)+1)) is equal to
Text Solution
|
int(dx)/(sinx+cosx) is equal to
Text Solution
|
The primitive of (1)/((x-a)^(3//2)(b-x)^(1//2)) is
Text Solution
|
If f(x) is the primitive of (sin 3sqrt(x)log(1+3x))/((tan^(-1)sqrt(x))...
Text Solution
|
If the primitive of f(x) = (1)/(3 sin x + sin^(3) x) is equal to f(x) ...
Text Solution
|
The value of int (cos x)/(sin x + cos x) dx is
Text Solution
|
If the primitive of (1)/(e^(x)-1)^(2) is f(x) - log |g (x)| + C then
Text Solution
|
If (dx)/(sin^(4)x+cos^(4)x)=(1)/(sqrt(2))tan^(-1)f(x)+C
Text Solution
|
The 1int(sin^(2)x)/(cos^(6)x)dx is a
Text Solution
|
If int tan^(7) x dx = f(x) + C then
Text Solution
|
If int(dx)/(sin x cos x)=log|f(x)|+C then
Text Solution
|