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underset(pi//4)overset(pi//2)(int) cosec...

`underset(pi//4)overset(pi//2)(int) cosec^(2)xdx=....`

A

`-1`

B

1

C

0

D

`1//2`

Text Solution

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The correct Answer is:
B
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Prove that underset(-a)overset(a)int f(x)dx={{:(,2underset(0)overset(a)int f(x)dx,"if f(x) is an even function"),(,0,"if f(x) is an odd function"):} and hence evaluate underset(-pi//2)overset(pi//2)int (x^(3)+x cos x)dx.

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KCET PREVIOUS YEAR PAPERS-KARNATAKA CET 2005-MATHEMATICS
  1. int(sin(2x)dx)/(1+cos^(2)x)=

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  2. inte^(x)((1+sinx)/(1+cosx))dx=

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  3. int (1 + tan x)/(e^(-x). Cos x) dx =

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  4. underset(pi//4)overset(pi//2)(int) cosec^(2)xdx=....

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  5. underset(0)overset(pi//4)(int)log(1+tanx)dx=.....

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  6. The modulus and amplitude of (1 + 2i)/(1-(1-i)^(2)) are

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  7. The real part of (1)/(1+cos theta+i sin theta) is

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  8. underset(xrarr0)(Lim)(tanx-sinx)/(x^(3)) is equal to...

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  9. If y = (e^(x)+e^(-x))/(e^(x)-e^(-x))then is equal to...

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  10. If f(x)={overset((sin^(5x))/(x^(2)+2x),xne0)underset(k+(1)/(2),x=0)is ...

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  11. The are bounded by the parabola y^(2)=4ax and the line x = a and x = 4...

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  12. A population p(t) of 1000 bacteria introduced into nutrient medium gro...

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  13. Form the differential equation of the family of circles touching the y...

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  14. The area of the region bounded by the curve9x^(2) + 4y^(2) - 36 = 0 is...

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  15. The general solution of the differential equation (2x - y + 1) dx + (2...

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  16. Ify = tan^(-1) ((sqrt(1+x^(2)) -sqrt(1-x^(2)))/(sqrt(1+x^(2)) + sqrt(1...

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  17. If x = sin t, y = cos pt then...

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  18. If ST and SN are the lengths of the subtangent and the subnormal at th...

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