हिंदी

Integrate the following w.r.t. x : x3 + x2 – x + 1 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

`int(x^3 + x^2 – x + 1)dx = int x3  dx + int x^2 dx - int x dx + int 1 dx`

= `x^4/(4) + x^3/(3) - x^2/(2) + x + c`.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Exercise 3.1 [पृष्ठ १०२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Indefinite Integration
Exercise 3.1 | Q 1.1 | पृष्ठ १०२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Evaluate : `int(x-3)sqrt(x^2+3x-18)  dx`


 
 

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

 
 

Integrate the functions:

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


Integrate the functions:

`e^(2x+3)`


Integrate the functions:

`(1+ log x)^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 (2y^2)/(y^2 + 4)dx`


\[\int\sqrt{2 x^2 + 3x + 4} \text{ dx}\]

Write a value of

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

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


Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]


Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]


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


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

 Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`


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


Evaluate the following integrals : tan2x dx


Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 


Evaluate the following integrals : `int sinx/(1 + sinx)dx`


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


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


Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`


Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`


Evaluate the following integrals:

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


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


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


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

cos8xcotx


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`


Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`


Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`


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


Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).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 f x^x (1 + log x)*dx`


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives :

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


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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int 1/("a"^2 - "b"^2 "x"^2)` 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


Evaluate `int "x - 1"/sqrt("x + 4")` dx


Evaluate: ∫ |x| dx if x < 0


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


`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________


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


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


`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`


`int cot^2x  "d"x`


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`


Evaluate  `int"e"^x (1/x - 1/x^2)  "d"x`


`int sin^-1 x`dx = ?


`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.


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


`int (f^'(x))/(f(x))dx` = ______ + c.


Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.


Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.


Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`


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


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


Evaluate `int1/(x(x - 1))dx`


Evaluate the following.

`int x sqrt(1 + x^2)  dx`


Evaluate:

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


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


Evaluate:

`int(cos 2x)/sinx dx`


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


Evaluate the following.

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


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


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


Evaluate `int(1 + x + x^2 / (2!))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×