हिंदी

Find the following integrals: ∫(2x-3cosx+ex)dx

Advertisements
Advertisements

प्रश्न

Find the following integrals:

`int(2x - 3cos x + e^x) dx`

योग
Advertisements

उत्तर

Let `I = int (2x - 3  cos x + e^x)` dx

`I = 2 int x dx - 3 int cos x dx + int e^x` dx

`I = (2x^2)/2 - 3  sin x + e^x + C`

`I = x^2 - 3  sin x + e^x + C`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.1 [पृष्ठ २९९]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.1 | Q 16 | पृष्ठ २९९

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).


Find an anti derivative (or integral) of the following function by the method of inspection.

e2x


Find an anti derivative (or integral) of the following function by the method of inspection.

(axe + b)2


Find the following integrals:

`intx^2 (1 - 1/x^2)dx`


Find the following integrals:

`int (ax^2 + bx + c) dx`


Find the following integrals:

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


Find the following integrals:

`int(1 - x) sqrtx dx`


Find the following integrals:

`intsec x (sec x + tan x) dx`


Find the following integrals:

`int (2 - 3 sinx)/(cos^2 x) dx.`


If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.


Integrate the function:

`1/(x - x^3)`


Integrate the function:

`1/(x^2(x^4 + 1)^(3/4))`


Integrate the function:

`(5x)/((x+1)(x^2 +9))`


Integrate the function:

`(e^(5log x) -  e^(4log x))/(e^(3log x) - e^(2log x))`


Integrate the function:

`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`


Integrate the function:

`1/sqrt(sin^3 x sin(x + alpha))`


Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`


Integrate the function:

`sqrt((1-sqrtx)/(1+sqrtx))`


Integrate the function:

`tan^(-1) sqrt((1-x)/(1+x))`


`int (dx)/sqrt(9x - 4x^2)` equal


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


`int e^x sec x(1 + tanx) dx` equals


`int sqrt(1 + x^2) dx` is equal to


What is anti derivative of `e^(2x)`


`d/(dx)x^(logx)` = ______.


If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.


In \[\int f(x)\,dx\], what is \(f(x)\) called?


In \[\int f(x)\,dx\], what is \(x\) called?


What is integration?


Which statement about indefinite integrals is correct?


Which antiderivative has derivative \(1\)?


Which expression is also an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?


Evaluate \[\int \frac{dx}{1+x^2}\]


Evaluate \[\int e^x\,dx\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×