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7(int0^1(x^4(1-x)^4dx)/(1+x^2)+pi) is e...

`7(int_0^1(x^4(1-x)^4dx)/(1+x^2)+pi)` is equal to

A

`(22)/(7)-pi`

B

`(2)/(105)`

C

0

D

`(71)/(15)-(3pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`overset(1)underset(0)int (x^(4)(1-x)^(4))/(1+x^(2))dx`
`=overset(1)underset(0)int (x^(6)-4x^(5)+5x^(4)-4x^(2)+4-(4)/(1+x^(2)))dx`
`=(1)/(7)-(2)/(3)+1-(4)/(3)+4-4xx(pi)/(4)=(22)/(7)-pi`
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. int(-2)^(2) |[x]|dx=

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  2. The value int^(2)(-2) {p" In"((1+x)/(1-x))+q" In "((1-x)/(1+x))-2+r}...

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  3. 7(int0^1(x^4(1-x)^4dx)/(1+x^2)+pi) is equal to

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  4. The value of lim(x to 0)(1)/(x^(3))(t " In"(1+t))/(t^(4)+4)dt is

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  5. Let f be the function defined on [-pi,pi] given by f(0)=9 and f(x)=sin...

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  6. Let f be a real-valued function defind on the interval (-,1) such that...

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  7. For any real number x, let [x] denote the largest integer less than or...

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  8. Let of a real-valued function defined on the interval(0,oo) by f(x)=In...

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  9. Let p(x) be a function defined on R such that p'(x)=p' for all z in[0,...

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  10. If int(a)^(b) {f(x)-3x}dx=a^(2)-b^(2), then the value of f((pi)/(6)), ...

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  11. The value of (pi^(2))/("In"3)int(7//6)^(5//6) sec(pix)dx is

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  12. The value of the integral int(-pi//2)^(pi//2) {x^(2)+log((pi+x)/(pi-...

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  13. Let f:(0,1) in (0,1) be a differenttiable function such that f(x)ne 0 ...

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  14. The value of the integral int(0)^(2) (log(x^(2)+2))/((x+2)^(2)), dx is

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  15. The integral int(pi//4)^(pi//2) (2 cosecx)^(17)dx is equal to

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  16. Let f:[0,2] in R be a function which is continuous on [0,2] and is dif...

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  17. Given that for each a in (0,1) lim^(h to 0^(+)) int(h)^(1-h) t^(-a)(1...

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  18. Given that for each a in (0,1)lim(x to 0) int(h)^(-h) t^(-a)(1-t)^(a-1...

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  19. The options (s) with the values of a and L that satisfy the following ...

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  20. Let f:R to R be a continuous odd function, which vanishes exactly at o...

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