मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Indefinite Integration - Exercise 3.1 [पृष्ठ १०२]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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


Integrate the functions:

`sqrt(ax + b)`


Integrate the functions:

`xsqrt(1+ 2x^2)`


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

`1/(1 - tan x)`


Integrate the functions:

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


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


Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

\[\int\frac{\cos^5 x}{\sin x} \text{ dx }\]

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


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

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


Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`


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

`(1)/(sinx.cosx + 2cos^2x)`


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


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


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


Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`


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


Choose the correct options from the given alternatives :

`int (e^x(x - 1))/x^2*dx` =


Evaluate the following.

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


Evaluate the following.

∫ (x + 1)(x + 2)7 (x + 3)dx


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


Choose the correct alternative from the following.

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


Fill in the Blank.

`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c


Fill in the Blank.

`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______


State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t


State whether the following statement is True or False.

If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`


Evaluate: `int log ("x"^2 + "x")` dx


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int (7x + 9)^13  "d"x` ______ + c


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


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.


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


The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.


`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`


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


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


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


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


Evaluate.

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


Evaluate the following:

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


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


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


After choosing \[u=g(x)\], what is the next step?


What must be done before integrating after obtaining \[du\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×