मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Evaluate ∫(3x2-5)2 dx

Advertisements
Advertisements

प्रश्न

Evaluate `int(3x^2 - 5)^2  "d"x`

बेरीज
Advertisements

उत्तर

Let I = `int(3x^2 - 5)^2  "d"x`

= `int (9x^4 - 30x^2 + 25) "d"x`

= `9intx^4"d"x - 30int x^2"d"x + 25int"d"x`

= `9((x^5)/5) - 30((x^3)/3) + 25x + "c"`

∴ I = `9/5 x^5 - 10x^3 + 25x + "c"`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.5: Integration - Q.4

संबंधित प्रश्‍न

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


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

Write a value of

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

Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]


Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`


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


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


Evaluate the following integrals:

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


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


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


Evaluate the following.

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


Evaluate the following.

`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt


Evaluate the following.

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


Choose the correct alternative from the following.

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


Fill in the Blank.

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


To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.


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 x^x (1 + logx)  "d"x`


`int 1/(xsin^2(logx))  "d"x`


`int (7x + 9)^13  "d"x` ______ + c


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


`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`


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


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


Evaluate:

`int 1/(1 + cosα . cosx)dx`


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


Evaluate:

`intsqrt(sec  x/2 - 1)dx`


Integration by substitution is the reverse process of which rule?


When applying substitution, what must always be rewritten in terms of the new variable?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×