मराठी

Evaluate the following: d∫sinx+cosx1+sin2xdx - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`

बेरीज
Advertisements

उत्तर

I = `int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`

= `int (sinx + cosx)/sqrt(sin^2x + cos^2x + 2 sin x cosx) "d"x`

= `int (sin x + cosx)/sqrt((sinx + cosx)^2) "d"x`

= `int 1"d"x`

= x + C

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Integrals - Exercise [पृष्ठ १६४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 7 Integrals
Exercise | Q 8 | पृष्ठ १६४

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`


Find the integrals of the function:

cos 2x cos 4x cos 6x


Find the integrals of the function:

sin3 x cos3 x


Find the integrals of the function:

sin 4x sin 8x


Find the integrals of the function:

`(1-cosx)/(1 +  cos x)`


Find the integrals of the function:

`cos x/(1 + cos x)`


Find the integrals of the function:

`(sin^2 x)/(1 + cos x)`


Find the integrals of the function:

tan3 2x sec 2x


Find the integrals of the function:

tan4x


Find the integrals of the function:

`1/(sin xcos^3 x)`


Find the integrals of the function:

`(cos 2x)/(cos x + sin x)^2`


Find the integrals of the function:

sin−1 (cos x)


Find the integrals of the function:

`1/(cos(x - a) cos(x - b))`


`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.


`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.


Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`


Find `int_  (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `


Find `int_  sin ("x" - a)/(sin ("x" + a )) d"x"`


Find `int_  (log "x")^2 d"x"`


Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration. 


Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`


Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`


Find `int "dx"/(2sin^2x + 5cos^2x)`


Find `int x^2tan^-1x"d"x`


`int "e"^x (cosx - sinx)"d"x` is equal to ______.


`int (sin^6x)/(cos^8x) "d"x` = ______.


Evaluate the following:

`int ("d"x)/(1 + cos x)`


Evaluate the following:

`int (cosx - cos2x)/(1 - cosx) "d"x`


Evaluate the following:

`int sin^-1 sqrt(x/("a" + x)) "d"x`  (Hint: Put x = a tan2θ)


`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.


`int sinx/(3 + 4cos^2x) "d"x` = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×