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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫12e1xx2 dx = - Mathematics and Statistics

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प्रश्न

`int_1^2 ("e"^(1/x))/(x^2)  "d"x` =

पर्याय

  • `2sqrt("e")(1 + sqrt("e"))`

  • `sqrt("e")(1 - sqrt("e"))`

  • `sqrt("e")(sqrt("e") - 1)`

  • `sqrt("e")(1 + sqrt("e"))`

MCQ

उत्तर

`sqrt("e")(sqrt("e") - 1)`

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Fundamental Theorem of Integral Calculus
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.4: Definite Integration - MCQ

संबंधित प्रश्‍न

Evaluate : `int_0^(pi/4) sin^4x*dx`


Evaluate : `int_0^4 (1)/sqrt(4x - x^2)*dx`


Evaluate:

`int_0^1 (1)/sqrt(3 + 2x - x^2)*dx`


Evaluate : `int_0^1 x tan^-1x*dx`


Evaluate : `int_0^(pi//4) (sin2x)/(sin^4x + cos^4x)*dx`


Evaluate:

`int_0^(pi/2) sqrt(cos x) sin^3x * dx`


Evaluate:

`int_0^1 sqrt((1 - x)/(1 + x)) * dx`


Evaluate the following : `int_0^3 x^2(3 - x)^(5/2)*dx`


Evaluate the following : `int_1^oo 1/(sqrt(x)(1 + x))*dx`


Evaluate the following : `int_0^(pi/2) [2 log (sinx) - log (sin 2x)]*dx`


Evaluate the following : `int_0^4 [sqrt(x^2 + 2x + 3]]^-1*dx`


Evaluate the following definite integrals: if `int_1^"a" (3x^2 + 2x + 1)*dx` = 11, find a.


Evaluate the following integrals:

`int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx`


Evaluate the following integrals : `int_1^2 sqrt(x)/(sqrt(3 - x) + sqrt(x))*dx`


Choose the correct alternative :

If `int_0^"a" 3x^2*dx` = 8, then a = ?


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Solve the following : `int_2^3 x/(x^2 - 1)*dx`


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Prove that: `int_"a"^"b" "f"(x)  "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`


Prove that: `int_0^(2"a") "f"(x)  "d"x = int_0^"a" "f"(x)  "d"x + int_0^"a" "f"(2"a" - x)  "d"x`


`int_0^"a" 4x^3  "d"x` = 81, then a = ______


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Evaluate `int_0^1 "e"^(x^2)*"x"^3  "d"x`


By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2))  "d"x`

Solution: Let I = `int_1^2 (x + 3)/(x(x + 2))  "d"x`

Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`

∴ x + 3 = A(x + 2) + B.x

∴ A = `square`, B = `square`

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∴ I = `[square log x + square log(x + 2)]_1^2`

∴ I = `square`


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Evaluate the following definite integral:

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`int_0^1 e^(x^2) x^3  dx`


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`int_-9^9 x^3/(4-x^2)` dx


Evaluate the following definite intergral:

`int_1^2 (3x)/ ((9x^2 -1)) dx`


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Evaluate the integral.

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Solve the following.

`int_0^1e^(x^2) x^3 dx`


Evaluate the following definite integral:

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