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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫0π2log(tanx) dx = - Mathematics and Statistics

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प्रश्न

`int_0^(pi/2) log(tanx)  "d"x` =

पर्याय

  • `pi/8(log2)`

  • 0

  • `- pi/8 (log2)`

  • `pi/2 (log2)`

MCQ

उत्तर

0

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Methods of Evaluation and Properties of Definite Integral
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.4: Definite Integration - MCQ

संबंधित प्रश्‍न

Evaluate: `int_0^(π/4) cot^2x.dx`


Evaluate: `int_0^1 (x^2 - 2)/(x^2 + 1).dx`


Evaluate: `int_0^oo xe^-x.dx`


Evaluate the following:

`int_0^a (1)/(x + sqrt(a^2 - x^2)).dx`


Choose the correct option from the given alternatives : 

`int_0^(pi/2) (sin^2x*dx)/(1 + cosx)^2` = ______.


If `int_0^1 ("d"x)/(sqrt(1 + x) - sqrt(x)) = "k"/3`, then k is equal to ______.


`int_(pi/5)^((3pi)/10)  sinx/(sinx + cosx)  "d"x` =


`int_0^1 (x^2 - 2)/(x^2 + 1)  "d"x` =


Let I1 = `int_"e"^("e"^2)  1/logx  "d"x` and I2 = `int_1^2 ("e"^x)/x  "d"x` then 


Evaluate: `int_(- pi/4)^(pi/4) x^3 sin^4x  "d"x`


Evaluate: `int_0^(pi/4) sec^2 x  "d"x`


Evaluate: `int_0^1 |x|  "d"x`


Evaluate: `int_0^1 "e"^x/sqrt("e"^x - 1)  "d"x`


Evaluate: `int_0^(pi/2)  (sin2x)/(1 +  sin^2x)  "d"x`


Evaluate: `int_0^(pi/2) cos^3x  "d"x`


Evaluate: `int_0^(pi/4) (tan^3x)/(1 + cos 2x)  "d"x`


Evaluate: `int_0^(pi/4)  cosx/(4 - sin^2 x)  "d"x`


Evaluate: `int_1^3 (cos(logx))/x  "d"x`


Evaluate: `int_0^9 sqrt(x)/(sqrt(x) + sqrt(9 - x)  "d"x`


Evaluate: `int_0^(pi/2) (sin^4x)/(sin^4x + cos^4x)  "d"x`


Evaluate: `int_3^8 (11 - x)^2/(x^2 + (11 - x)^2)  "d"x`


Evaluate: `int_(-4)^2 1/(x^2 + 4x + 13)  "d"x`


Evaluate: `int_0^1 1/sqrt(3 + 2x - x^2)  "d"x`


Evaluate: `int_0^1 x* tan^-1x  "d"x`


Evaluate: `int_0^(pi/4) sec^4x  "d"x`


Evaluate: `int_(-1)^1 1/("a"^2"e"^x + "b"^2"e"^(-x))  "d"x`


Evaluate: `int_0^"a" 1/(x + sqrt("a"^2 - x^2))  "d"x`


Evaluate: `int_0^(1/2) 1/((1 - 2x^2) sqrt(1 - x^2))  "d"x`


Evaluate: `int_(1/sqrt(2))^1  (("e"^(cos^-1x))(sin^-1x))/sqrt(1 - x^2)  "d"x`


Evaluate: `int_(-1)^1 (1 + x^2)/(9 - x^2)  "d"x`


Evaluate:

`int_(π/4)^(π/2) cot^2x  dx`.


Evaluate:

`int_0^(π/2) sin^8x  dx`


Evaluate `int_(π/6)^(π/3) cos^2x  dx`


The value of `int_2^(π/2) sin^3x  dx` = ______.


Evaluate:

`int_0^(π/2) (sin 2x)/(1 + sin^4x)dx`


`int_0^1 x^2/(1 + x^2)dx` = ______.


Find the value of ‘a’ if `int_2^a (x + 1)dx = 7/2`


Evaluate:

`int_0^(π/2) sinx/(1 + cosx)^3 dx`


Evaluate `int_(-π/2)^(π/2) sinx/(1 + cos^2x)dx`


If `int_0^π f(sinx)dx = kint_0^π f(sinx)dx`, then find the value of k.


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