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underset(0)overset(pi//2)(dx)/(4+5cosx)...

`underset(0)overset(pi//2)(dx)/(4+5cosx)`

Text Solution

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The correct Answer is:
`1/3 ln2`
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underset(0)overset(pi//2)(sin^(5)x)/(sin^(5)x+cos^(5)x) dx

Evaluate the integral int_(0)^(pi//2) (dx)/(4+5cosx )

Knowledge Check

  • underset(r=0)overset(10)sum (40-r)C_(5)=

    A
    `""^(41)C_(5)-""^(30)C_(5)`
    B
    `""^(41)C_(6)-""^(30)C_(6)`
    C
    `""^(41)C_(5)+""^(30)C_(5)`
    D
    `""^(41)C_(6)`

  • In the following carbocation , H//CH_3 that is most likely to migrate to the positively charged carbon is -H-underset(H)underset(|)overset(H)overset(|1)(C )-underset(HO)underset(|)overset(H)overset(|2)(C )-underset(H)underset(|)overset(o+)(C )-underset(H)underset(|)overset(H)overset(|4)(C )-overset(5)(C )H_3

    A
    `CH_3` at `C - 4`
    B
    `H` at `C - 4`
    C
    `CH_3` at `C - 2`
    D
    `H` at `C - 2`

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    Evaluate int_(0)^(pi"/"2) (dx)/(4 + 5 cos x)

    int_(0)^(pi//2)(5+4cosx)/((4+5cosx)^(2))dx=

    HCHO underset(Ni)overset(H_(2))rarr A overset(PCl_(5))rarr B underset(KCN)overset("Alcoholic")rarr C underset(C_(2)H_(5)OH)overset(Na)rarr D underset(HCl)overset(NaNO_(2))rarr E underset(H_(2)SO_(4))overset(K_(2)O_(2)O_(7))rarr F . Write the isomer of the product 'F'

    Evaluate the definite integrals . I=underset(0)overset(1)int x. e^(-x^(2))dx

    Explain how the hybrid structure is related to the structures of each of the following pairs of contributing resonance structures? (a) overset(oplus)(C )H_(2) underset((i))- underset(..)overset(Θ)C H_(2) harr CH_(2) underset((ii))= CH_(2) (b) H_(2)C underset((iii))= overset(..)(O): harr H_(2)C underset((iv))- underset(..)overset(..)O:^(-) (c ) R_(2) overset(+)C- underset(underset(underset((v))(R ))(|))C= overset(..)O: harr underset((vi))(R_(2)C = underset(underset(R )(|))(C) - overset(..)O:^(+)) (d) underset((VII)) (R-C^(+) = overset(..)(O): )harr underset((VIII))(R-C-= O:^(+)) (e ) underset((IX))(R- underset(underset( :O: )(||))(C)- underset(..)overset(..)OH) harr underset((IX))(R- underset(underset( :underset(..)(O): )(|))(C) - ""^(oplus")underset(..)OH)

    int_(0)^(pi//2)(cosx)/(1+sinx)dx=

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