मराठी

Ndnn∫0π2sinnxdxsinnx+cosnx = ______.

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प्रश्न

`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.

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उत्तर

`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = `pi/4`.

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पाठ 7: Integrals - Solved Examples [पृष्ठ १६३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 7 Integrals
Solved Examples | Q 32 | पृष्ठ १६३

संबंधित प्रश्‍न

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Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`


 
 

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

 
 

By using the properties of the definite integral, evaluate the integral:

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


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`int_2^8 |x - 5| dx`


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Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`


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By completing the following activity, Evaluate `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x))  "d"x`.

Solution: Let I = `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x))  "d"x`     ......(i)

Using the property, `int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`, we get

I = `int_2^5 ("(  )")/(sqrt(7 - x) + "(  )")  "d"x`   ......(ii)

Adding equations (i) and (ii), we get

2I = `int_2^5 (sqrt(x))/(sqrt(x) - sqrt(7 - x))  "d"x + (   )  "d"x`

2I = `int_2^5 (("(    )" + "(     )")/("(    )" + "(     )"))  "d"x`

2I = `square`

∴ I =  `square`


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Solve the following.

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


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`int_0^sqrt(2)[x^2]dx`


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