English

Integrate the functions: sec2(7 – 4x)

Advertisements
Advertisements

Question

Integrate the functions:

sec2(7 – 4x)

Sum
Advertisements

Solution

Let `I = int sec^2` (7 - 4x) dx

Put 7 - 4x = t

- 4 dx = dt or dx `= - 1/4` dt

Hence, `I = - 1/4 int sec^2` t dt

`= - 1/4` tan t + C

`= - 1/4` tan (7 - 4x) + C

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.2 [Page 305]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.2 | Q 22 | Page 305

RELATED QUESTIONS

Find: `int(x+3)sqrt(3-4x-x^2dx)`


 
 

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

 
 

Integrate the functions:

`sin x/(1+ cos x)`


Integrate the functions:

`1/(1 + cot x)`


Write a value of

\[\int\frac{1 + \cot x}{x + \log \sin x} \text{ dx }\]

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

Write a value of

\[\int e^x \sec x \left( 1 + \tan x \right) \text{ dx }\]

Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .


Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`


Integrate the following function w.r.t. x:

x9.sec2(x10)


Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`


Integrate the following functions w.r.t. x:

`(sinx cos^3x)/(1 + cos^2x)`


Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`


Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`


Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


Evaluate the following : `int (logx)2.dx`


Evaluate the following.

`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx


Evaluate the following.

`int 1/(4"x"^2 - 1)` dx


Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`


Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx


Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx


To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.


Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx


`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________


`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________


`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`


`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?


`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`


`int (x + sinx)/(1 + cosx)dx` is equal to ______.


`int sqrt(x^2 - a^2)/x dx` = ______.


Evaluate the following.

`int x^3/(sqrt(1+x^4))dx`


Evaluate `int1/(x(x - 1))dx`


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate.

`int (5x^2 - 6x + 3)/(2x - 3) dx`


Evaluate the following.

`int x^3/sqrt(1+x^4) dx`


Evaluate the following

`int x^3 e^(x^2) ` dx


Evaluate:

`intsqrt(sec  x/2 - 1)dx`


For \[t=\cos x\], what is \[dt\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×