हिंदी

Evaluate the following : ∫12x2-5.dx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`

योग

उत्तर

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

=  `(1)/sqrt(2) int (1)/sqrt(x^2 - 5/2).dx`

= `(1)/sqrt(2) int (1)/sqrt(x^2 - (sqrt(5/2))^2).dx`

= `(1)/sqrt(2) log|x + sqrt(x^2 - 5/2)| + c`.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Exercise 3.2 (B) [पृष्ठ १२३]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Indefinite Integration
Exercise 3.2 (B) | Q 1.06 | पृष्ठ १२३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Integrate the functions:

`1/(x + x log x)`


Integrate the functions:

`x/(9 - 4x^2)`


Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


`int (dx)/(sin^2 x cos^2 x)` equals:


Write a value of

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

Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 


Write a value of

\[\int\frac{\cos x}{3 + 2 \sin x}\text{  dx}\]

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]


Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]


Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].


Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .


Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]


Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].


The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is


Integrate the following w.r.t. x : x3 + x2 – x + 1


Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`


Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


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


Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`


Integrate the following functions w.r.t. x : sin5x.cos8x


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


Evaluate the following : `int sinx/(sin 3x).dx`


Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`


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


Choose the correct options from the given alternatives :

`int sqrt(cotx)/(sinx*cosx)*dx` =


Choose the correct options from the given alternatives :

`int (e^(2x) + e^-2x)/e^x*dx` =


Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`


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


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


Evaluate the following.

`int (1 + "x")/("x" + "e"^"-x")` dx


Evaluate the following.

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


Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx


Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx


Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx


Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is


`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c


State whether the following statement is True or False.

If `int x  "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.


`int (sin4x)/(cos 2x) "d"x`


`int x^x (1 + logx)  "d"x`


`int 1/(xsin^2(logx))  "d"x`


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


`int dx/(1 + e^-x)` = ______


`int (cos x)/(1 - sin x) "dx" =` ______.


`int[ tan (log x) + sec^2 (log x)] dx= ` ______


`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.


`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.


The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.


If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.


The value of `sqrt(2) int (sinx  dx)/(sin(x - π/4))` is ______.


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


`int dx/(2 + cos x)` = ______.

(where C is a constant of integration)


Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.


Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.


Evaluated the following

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


if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`


Evaluate the following.

`int 1/(x^2 + 4x - 5)  dx`


Evaluate the following.

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


Evaluate:

`int sqrt((a - x)/x) dx`


Evaluate.

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


`int 1/(sin^2x cos^2x)dx` = ______.


`int (cos4x)/(sin2x + cos2x)dx` = ______.


The value of `int ("d"x)/(sqrt(1 - x))` is ______.


Evaluate the following

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×