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If u (n) = int (0) ^(pi//2) x ^(n) sin x...

If `u _(n) = int _(0) ^(pi//2) x ^(n) sin x dx, n in N` then the value of `u _(10) + 90 u _(s) ` is

A

`9 ((pi)/(2)) ^(8)`

B

` ((pi)/(2)) ^(9)`

C

`10 ((pi)/(2))^(9)`

D

`9 ((pi)/(2)) ^(9)`

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
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  7. Let I (1) = int (0) ^(1) (e ^(x) dx )/( 1 + x) and I (2) = int (0) ^(1...

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  8. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  9. If underset(0)overset(100)intf(x) dx = a, then underset(r=1)overset(10...

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  10. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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  11. underset(2-ln3)overset(3+ln3)int(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal...

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  12. If [x] stands for the greatest integer function, the value of overset(...

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  13. Find the value of the function f(x)=1+x+int1^x((lnt)^2+2lnt) dt where ...

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  14. If f(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4) then f^(prime)(2) has th...

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  15. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  16. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

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  17. lim( n to oo) (sin ""(pi)/(2n) . sin ""(2pi)/(2n). sin ""(3pi)/(2n)......

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  18. The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(...

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  19. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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  20. Evaluate : lim(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim(n->oo) (1^3+2^3...

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