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If f(x) = int(0)^(x) t cos t dt, then (d...

If `f(x) = int_(0)^(x) t cos t dt`, then `(df)/(dx)`

A

`1/2(1-x^(2))`

B

`1/2x^(2)`

C

`1/2(1+x^(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={(int_(-1)^(x)-tdt,-1lexlt0),(int_(-1)^(0)-tdt+int_(0)^(x)tdt, xge0):}={(1/2(1-x^(2)),-1lexlt0),(1/2(1+x^(2)),xge0):}`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. T h ev a l u eofint0^(pi/2)sin|2x-alpha|dx ,w h e r ealpha in [0,pi],i...

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  2. f(x) is a continuous function for all real values of x and satisfies i...

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  3. If f(x) = int(0)^(x) t cos t dt, then (df)/(dx)

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  4. If agt0 and A=int(0)^(a)cos^(-1)xdx, and int(-a)^(a)(cos^(-1)x-sin^(...

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  5. The value of int1^a[x]f^(prime)(x)dxf^(prime)(x)dx ,w h e r ea >1,a n ...

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  6. int3^(10)[log[x]]dxi se q u a lto(w h e r e[dot]r e p r e s e t n tt h...

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  7. int(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer...

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  8. T h ev a l u eofint(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes ...

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  9. Evaluate: int0^(2pi)[sinx]dx ,w h e r e[x] denotes the greatest integ...

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  10. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

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  11. G i v e nint0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integr...

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  12. "I f"I1=int(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I2=int(-10...

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  13. The value of int0^oo(x dx)/((1+x)(1+x^2)) is equal to

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  14. about to only mathematics

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  15. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)]dx , I2=i...

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  16. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I2=int(f...

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  17. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

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  18. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is sqrt(...

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  19. f(x)>0AAx in Ra n di sbou n d e ddotIf (lim)(nvecoo)[int0^a(f(x)dx)/...

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  20. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,t h e nlambdai s...

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