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

∫x21-x6 dx = ________________

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प्रश्न

`int x^2/sqrt(1 - x^6)` dx = ________________

पर्याय

  • −sin−1 (x3) + c

  • cos−1 (x3) + c

  • sin−1 (x3) + c

  • `1/3 sin^(-1) (x^3) + "c"`

MCQ
रिकाम्या जागा भरा
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उत्तर

`1/3 sin^(-1) (x^3) + "c"`

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Integrate the functions:

`1/(x + x log x)`


Integrate the functions:

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


Evaluate : `∫1/(3+2sinx+cosx)dx`


Evaluate: `int (sec x)/(1 + cosec x) dx`


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

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is


Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`


Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`


Evaluate the following integrals : `int sinx/(1 + sinx)dx`


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


Integrate the following functions w.r.t. x : tan5x


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


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


Evaluate the following.

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


Evaluate the following.

`int 1/("x" log "x")`dx


Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =


Choose the correct alternative from the following.

`int "dx"/(("x" - "x"^2))`= 


Evaluate `int "x - 1"/sqrt("x + 4")` dx


`int (log x)/(log ex)^2` dx = _________


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


`int cot^2x  "d"x`


`int x/(x + 2)  "d"x`


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


Evaluate `int(3x^2 - 5)^2  "d"x`


`int1/(4 + 3cos^2x)dx` = ______ 


The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.


The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.


Find `int dx/sqrt(sin^3x cos(x - α))`.


Evaluate the following.

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


Evaluate the following.

`int 1/(x^2+4x-5)  dx`


Evaluate the following.

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


Evaluate the following.

`int x sqrt(1 + x^2)  dx`


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


Evaluate the following.

`int(1)/(x^2 + 4x - 5)dx`


Evaluate.

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


Evaluate the following.

`int1/(x^2+4x-5) dx`


`int (cos4x)/(sin2x + cos2x)dx` = ______.


Evaluate the following:

`int (1) / (x^2 + 4x - 5) dx`


Evaluate the following.

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


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


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


What is integration by substitution?


Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?


For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?


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