हिंदी

Evaluate the following : ∫111-4x2.dx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`

योग

उत्तर

`int (1)/sqrt(11 - 4x^2).dx`

= `int (1)/sqrt((sqrt(11))^2 - (2x)^2).dx`

= `(1)/(2) sin^-1 (2x/sqrt(11)) + 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 1.05 | पृष्ठ १२३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`


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


Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`


Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.


Evaluate :   `∫1/(cos^4x+sin^4x)dx`


Integrate the functions:

`(log x)^2/x`


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

cot x log sin x


Integrate the functions:

`1/(1 - tan x)`


Integrate the functions:

`(1+ log x)^2/x`


Integrate the functions:

`((x+1)(x + logx)^2)/x`


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


Evaluate `int 1/(3+ 2 sinx + cosx) dx`


Evaluate: `int (sec x)/(1 + cosec x) dx`


\[\int\sqrt{1 + x - 2 x^2} \text{ dx }\]

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]

 Write a valoue of \[\int \sin^3 x \cos x\ dx\]

 


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


Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]


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


\[\text{ If } \int\left( \frac{x - 1}{x^2} \right) e^x dx = f\left( x \right) e^x + C, \text{ then  write  the value of  f}\left( x \right) .\]

\[If \int e^x \left( \tan x + 1 \right)\text{ sec  x  dx } = e^x f\left( x \right) + C, \text{ then  write  the value  of  f}\left( x \right) .\]

 

 


Evaluate the following integrals : `int sin x/cos^2x dx`


Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`


Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`


Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`


Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`


Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`


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

cos8xcotx


Evaluate the following integrals :  `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`


Evaluate the following integrals:

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


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


Choose the correct options from the given alternatives : 

`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =


`int logx/(log ex)^2*dx` = ______.


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


Integrate the following with respect to the respective variable:

`x^7/(x + 1)`


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


Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx


Evaluate the following.

∫ (x + 1)(x + 2)7 (x + 3)dx


Evaluate the following.

`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx


Choose the correct alternative from the following.

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


Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =


If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______


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`.


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx


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


If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int cot^2x  "d"x`


`int x/(x + 2)  "d"x`


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


`int (7x + 9)^13  "d"x` ______ + c


State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`


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


`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


`int(sin2x)/(5sin^2x+3cos^2x)  dx=` ______.


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

(where C is a constant of integration)


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


Evaluate the following.

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


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


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


Evaluate the following.

`intx sqrt(1 +x^2)  dx`


Evaluate the following.

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


Evaluate the following:

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


Evaluate the following:

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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


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


Evaluate:

`intsqrt(sec  x/2 - 1)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×