हिंदी

If f'(x) = x+1x, then f(x) is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

If f'(x) = `x + 1/x`, then f(x) is ______.

विकल्प

  • `x^2 + log |x| + C`

  • `x^2/2 + log |x| + C`

  • `x/2 + log |x| + C`

  • `x/2 - log |x| + C`

MCQ
रिक्त स्थान भरें

उत्तर

If f'(x) = `x + 1/x`, then f(x) is `underline(bb(x^2/2 + log |x| + C))`.

Explanation:

`x^2/2 + log |x| + C`  .....`(∵ f(x) = int(x + 1/x)dx)`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2022-2023 (March) Sample

संबंधित प्रश्न

Integrate the functions:

`(x^3 - 1)^(1/3) x^5`


Integrate the functions:

`x^2/(2+ 3x^3)^3`


Evaluate the following integrals : `int tanx/(sec x + tan x)dx`


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


Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`


Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`


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

`x^5sqrt(a^2 + x^2)`


Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`


Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`


Evaluate the following:

`int (1)/sqrt((x - 3)(x + 2)).dx`


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


Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`


Evaluate the following integrals:

`int (7x + 3)/sqrt(3 + 2x - x^2).dx`


Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =


Integrate the following w.r.t.x : `(3x + 1)/sqrt(-2x^2 + x + 3)`


If f'(x) = 4x3 − 3x2  + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).


`int cot^2x  "d"x`


`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`


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


`int (sin  (5x)/2)/(sin  x/2)dx` is equal to ______. (where C is a constant of integration).


If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.


Evaluate `int (1+x+x^2/(2!))dx`


Evaluate `int(1 + x + x^2/(2!))dx`


Prove that:

`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.


Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`


Evaluate the following.

`intxsqrt(1+x^2)dx`


Evaluate the following.

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


Evaluate.

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


Evaluate the following.

`int1/(x^2+4x-5)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×