English

Evaluate the definite integral: ∫0π4tanxdx

Advertisements
Advertisements

Question

Evaluate the definite integral:

`int_0^(pi/4) tan x dx`

Sum
Advertisements

Solution

`int_0^(pi/4)  tan x  dx`

`= [log sec x]_0^(pi/4)`

`= log sec  pi/4 - log sec 0`

`= log sqrt2 - log 1`

`= log sqrt2 = log 2^(1/2)`

`= 1/2  log 2`

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.9 [Page 338]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.9 | Q 7 | Page 338

RELATED QUESTIONS

If `int_0^h1/(2+8x^2)dx=pi/16 `then find the value of h.


 
 

Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)dx`

 
 

Evaluate the definite integral:

`int_(-1)^1 (x + 1)dx`


Evaluate the definite integral:

`int_(pi/6)^(pi/4) cosec x  dx`


Evaluate the definite integral:

`int_0^1 dx/sqrt(1-x^2)`


Evaluate the definite integral:

`int_2^3 dx/(x^2 - 1)`


Evaluate the definite integral:

`int_0^(pi/2) cos^2 xdx`


Evaluate the definite integral:

`int_2^3 (xdx)/(x^2 + 1)`


Evaluate the definite integral:

`int_1^2 (5x^2)/(x^2 + 4x + 3)`


Evaluate the definite integral:

`int_0^(pi/4) (2 sec^2 x + x^3  + 2) dx`


Evaluate the definite integral:

`int_0^pi (sin^2  x/2 - cos^2  x/2) dx`


`int_0^(2/3) dx/(4+9x^2)` equals:


Evaluate : \[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\] .


`int_6^(2/3) (dx)/(4 + 9x^2)` equals


Evaluate:

`int_0^π(sin^4x + cos^4x)dx`


If \(f\) is continuous on an interval, which expression defines the area function?


What does \[A(x)=\int_a^x f(t)\,dt\] give?


If \(f\) is continuous on \([a,b]\) and \[A(x)=\int_a^x f(t)\,dt,\] what is \(A'(x)\) for every \(x\) in \((a,b)\)?


Which condition permits direct use of the First Fundamental Theorem and the Second Fundamental Theorem on \([a,b]\)?


Why is there no need to write the constant of integration \(C\) while evaluating a definite integral?


Which expression correctly applies the limits to a definite integral?


Under the substitution \[30-x^{\frac32}=t,\] what is the correct expression for \(\sqrt{x}\,dx\)?


An antiderivative of \[\frac{\sqrt{x}}{(30-x^{\frac32})^2}\] is:


Evaluate \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx.\]


Which function is an antiderivative of \[\sin^3 2t\cos 2t?\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×