हिंदी

Integrate the following function w.r.t. x: x9.sec2(x10) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

x9.sec2(x10)

Evaluate:

`intx^9 . sec^2 (x^10) dx`

मूल्यांकन
योग
Advertisements

उत्तर

Let I = `int x^9 .sec^2(x^10).dx`

Put x10 = t
∴ 10x9dx = dt

∴ x9dx = `(1)/(10)dt`

∴ I = `int sec^2t.dt/(10)`

= `1/10 int sec^2t  dt`

= `(1)/(10)tan t+ c`

= `(1)/(10)tan(x^10) + c`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Exercise 3.2 (A) [पृष्ठ ११०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 3 Indefinite Integration
Exercise 3.2 (A) | Q 1.11 | पृष्ठ ११०

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`


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


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


Integrate the functions:

`xsqrt(x + 2)`


Integrate the functions:

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


Integrate the functions:

`(e^(2x) - 1)/(e^(2x) + 1)`


Integrate the functions:

`(e^(2x) -  e^(-2x))/(e^(2x) + e^(-2x))`


Integrate the functions:

`1/(cos^2 x(1-tan x)^2`


Integrate the functions:

`1/(1 + cot x)`


Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


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

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

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


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


Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 


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


Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`


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

`(5 - 3x)(2 - 3x)^(-1/2)`


Evaluate the following:

`int (1)/(25 - 9x^2)*dx`


Evaluate the following : `(1)/(4x^2 - 20x + 17)`


Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`


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


Evaluate the following.

`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx


Evaluate the following.

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


Evaluate the following.

`int 1/(x(x^6 + 1))` dx 


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


Choose the correct alternative from the following.

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


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


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


Evaluate `int (5"x" + 1)^(4/9)` dx


Evaluate: `int log ("x"^2 + "x")` dx


Evaluate: `int "e"^sqrt"x"` dx


`int 1/(cos x - sin x)` dx = _______________


`int sqrt(x^2 + 2x + 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 = ______


Evaluate `int(3x^2 - 5)^2  "d"x`


If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.


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


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


Evaluate the following.

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


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate.

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


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


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


Evaluate:

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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×