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Evaluate the following integral: int(-pi...

Evaluate the following integral: `int_(-pi//2)^pisin^(-1)(sin x)dx`

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I=`int_(-pi//2)^pisin^(-1)(sin x)dx`
I=`int_(-pi//2)^pi xdx`
I=`(x^2/2)_(-pi//2)^pi`
=`1/2(pi^2-pi^2/4)`
=`1/2(3pi^2/4)`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^4(|x|+|x-2|+|x-4|)dx\

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  2. Evaluate the following integral: int(-2)^2x e^(|x|)dx

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  3. Evaluate the following integral: int(-pi//2)^pisin^(-1)(sin x)dx

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  4. Evaluate the following integral: int(-3)^3|x+1|dx

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  5. Evaluate the following integral: int(-1)^2|2x+3|dx

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  6. Evaluate the following integral: int0^3|3x-1|dx

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  7. Evaluate the following integral: int(-2)^2|x+1|dx

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  8. Evaluate the following integral: int(-pi//4)^(pi//4)|s in x|dx

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  9. Evaluate the following integral: int(-pi//2)^(pi//2)|sinx+"cosx|dx

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  10. Evaluate the following integral: int1^4{|x-1|+|x-2|+|x-4|}dx

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  11. Evaluate the following integral: int(-pi//2)^(pi//2)(2sin|x|+cos x)dx

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  12. Evaluate of each of the following integral: int0^(2pi)(dx)/(e^(sinx)+1...

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  13. Evaluate of each of the following integral: int(-pi//4)^(pi//4)(tan^2x...

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  14. Evaluate of each of the following integral: int(-pi//3)^(pi//3)1/(1+e^...

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  15. Evaluate of each of the following integral: int0^(pi//2)(2logcos x-log...

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  16. Evaluate of each of the following integral: int(pi//6)^(pi//3)1/(1+sqr...

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  17. Evaluate of each of the following integral: int(-pi//2)^(pi//2)(cos^2x...

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  18. Evaluate of each of the following integral: inta^b(x^(1//n))/(x^(1//n)...

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  19. Evaluate of each of the following integral: int0^a(sqrt(x))/(sqrt(x)+s...

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  20. If f(a+b-x)=f(x),\ then prove that\ inta^b xf(x)dx=(a+b)/2inta^bf(x)d...

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