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f(x)=|{:(sec x,cos x,,sec^(2) x+cosecx c...

f(x)`=|{:(sec x,cos x,,sec^(2) x+cosecx cot x),(cos^(2) x,cos^(2) x,,cosec^(2) x),(1,cos^(2) x,, cos^(2) x):}|` then,
`int_(0)^(pi//2) `f(x) dx equals

A

0

B

1

C

`-((pi)/(4)+(8)/(15))`

D

-1

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If 0 lt a lt 1, then int(-1)^(1) (1)/(sqrt(1-2ax+a^(2)))dx is equal to

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  2. The value of int(0)^(pi//2) (x+sin x)/(1+cos x)dx, is

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  3. f(x)=|{:(sec x,cos x,,sec^(2) x+cosecx cot x),(cos^(2) x,cos^(2) x,,co...

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  4. If a is a fixed real number such that f(a-x)+f(a+x)=0, then int(0)^(2a...

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  5. The value of int(0)^(1) log((4+3 sin x)/(4+3 cos x))dx, is

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  6. The value of int(0)^(1) tan^(-1)((2x-1)/(1+x-x^(2)))dx is

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  7. The value of int(0)^(2pi) |cos x -sin x|dxis

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  8. If I(1)=int(0)^(1) 2^(x^(2)) dx, I(2)=int(0)^(1) 2^(x^(3)) dx, I(3)=in...

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  9. Consider the integrals I(1)=int(0)^(1)e^(-x)cos^(2)xdx,I(2)=int(0)^(...

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  10. If f(x)=f(a+b-x) for all x in[a,b] and int(a)^(b) xf(x) dx=k int(a)^(b...

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  11. To find the numberical value of int(-2)^(2) (px^(3)+qx+8)dx it is nece...

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  12. Let f:R to R be continuous functions. Then the value of the integral i...

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  13. The value of int(-1//2)^(1//2) |xcos((pix)/(2))|dx is

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  14. The value of the integral int(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

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  15. The value of int(pi//2)^0 (1)/(9 cosx+12 sinx)dx is

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  16. If I=int(3)^(4) (1)/(3sqrt(logx))dxthen

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  17. If I=int(0)^(1//2) (1)/(sqrt(1-x^(2n)))dxthen which one of the follow...

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  18. If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dxthen which one of the foll...

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  19. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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  20. The value of the integral int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal...

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