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If I(10) = int0^(pi/2) x^(10) sin x dx t...

If `I_(10) = int_0^(pi/2) x^(10) sin x dx` then `I_(10) + 90I_(8) =`

A

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

B

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

C

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

D

`(pi/2)^(9)`

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int0^(2pi) theta sin^2 theta cos theta d theta is equal to :

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  2. The value of integral int(-pi//4)^(pi//4) sin^(-4) x dx is :

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  3. If I(10) = int0^(pi/2) x^(10) sin x dx then I(10) + 90I(8) =

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  4. Let A = int0^(1) e^(t)/(t+1) dt, then int0^(1) (t.e^(t^(2)))/(t^(2)+1)...

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  5. If int0^(pi/2) (d theta)/(9 sin^(2) theta + 4 cos^(2) theta) = k pi, t...

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  6. Let f(x) = (e^(x)+1)/(e^(x)-1) and int0^(1)( (e^(x)+1)/(e^(x)-1)) x dx...

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  7. If int(-1)^(4) f(x) dx = 4 and int(2)^(4) f(x) dx = 7 then int2^(-1) f...

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  8. int0^(1) (sin^(2)x+cos^(x))/(cos^(x)+sin^(x)) x^(5) dx =

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  9. If beta +2 int0^(1) x^(2)e^(-x^(2)) dx = int0^(1) e^(-x^(2), then beta...

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  10. int0^(4/pi) (3x^(2) sin (1/x) - x cos (1/x)dx =

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  11. int0^(sqrtlog (pi/2)) cos(e^(x^(2))).2xe^(x^(2)) dx =

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  12. int0^(pi/2) (cosx-sinx)/(1+sinx cosx) dx =

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  13. int(-1/2)^(1/2) [sin^(-1)(3x-4x^(3)) - cos^(-1) (4x^(3)-3x)] dx =

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  14. int(-2)^(1) cot^(-1) (1/x) dx =

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  15. I = int(-2)^(1) (tan^(-1)x+ cot^(-1)(1/x) dx

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  16. int 1^(oo) (e^(x+1)+e^(3-x))^(-1) dx =

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  17. int1^(2) (dx)/(x(1+x^(4))) =

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  18. I(n) = int0^(pi/4) tan^(n) x dx, n in N, then I(10)+I(8) =

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  19. int0^(pi) sin^(50)x.cos^(49)xdx=

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  20. int sqrtx. e^(sqrtx) dx =

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