हिंदी

Evaluate the definite integral: ∫01dx1+x2

Advertisements
Advertisements

प्रश्न

Evaluate the definite integral:

`int_0^1 dx/(1+x^2)`

योग
Advertisements

उत्तर

`int_0^1  dx/(1 + x^2)`

`= [tan^-1 x]_0^1`

`= tan^-1 (1) - tan^-1 0`

`= pi/4 - 0`

`= pi/4`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.9 [पृष्ठ ३३८]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.9 | Q 10 | पृष्ठ ३३८

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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_2^3 1/x dx`


Evaluate the definite integral:

`int_1^2 (4x^3 - 5x^2 + 6x + 9)  dx`


Evaluate the definite integral:

`int_0^(pi/2) cos 2x  dx`


Evaluate the definite integral:

`int_4^5 e^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_0^1 (2x + 3)/(5x^2 + 1) dx`


Evaluate the definite integral:

`int_0^1 x e^(x^2) dx`


Evaluate the definite integral:

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


Evaluate the definite integral:

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


Evaluate the definite integral:

`int_0^2 (6x +3)/(x^2 + 4)` dx


Evaluate the definite integral:

`int_0^1 (xe^x + sin  (pix)/4)`


`int_1^(sqrt3)dx/(1+x^2) ` equals:


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


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


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


If \(f\) is continuous on \([a,b]\) and \(F\) is any antiderivative of \(f\), which formula evaluates the definite integral?


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?


For \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx,\] which substitution is used?


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


For \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt,\] which substitution and differential relation are correct?


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


Evaluate \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt.\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×