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

If f(x) = gsin-1x1-x2,g(x)=esin-1x, then g∫f(x)⋅g(x)⋅dx = ______.

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प्रश्न

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.

पर्याय

  • `e^(sin^-1x)*(sin^-1 x - 1) + c`

  • `e^(sin^-1x)*(1 - sin^-1x) + c`

  • `e^(sin^-1x)*(sin^-1 x + 1) + c`

  • `-e^(sin^-1x)*(sin^-1 x + 1) + c`

MCQ
रिकाम्या जागा भरा
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उत्तर

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = `underlinebb(e^(sin^-1x)*(sin^-1 x - 1) + c)`.

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:

(A) 0

(B) π

(C) π/2

(D) π/4


`int1/xlogxdx=...............`

(A)log(log x)+ c

(B) 1/2 (logx )2+c

(C) 2log x + c

(D) log x + c


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Choose the correct options from the given alternatives :

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Evaluate the following.

`int x^2 e^4x`dx


Evaluate the following.

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


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`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.


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Evaluate the following:

`int_0^pi x log sin x "d"x`


`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.


`int tan^-1 sqrt(x)  "d"x` is equal to ______.


Find: `int e^x.sin2xdx`


Solve: `int sqrt(4x^2 + 5)dx`


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Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.


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Evaluate:

`intcos^-1(sqrt(x))dx`


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`int e^(logcosx)dx`


Evaluate the following.

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


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


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`inte^x "cosec"  x(1 - cot x)dx`


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


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