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If (d(f(x)))/(dx) = g(x) AA x in [a, b] ...

If `(d(f(x)))/(dx) = g(x) AA x in [a, b]` then `int_(a)^(b)f(x).g(x)dx` is equal to :

A

`f(b)-f(a)`

B

`g(b)-g(a)`

C

`([f(b)]^(2)-[f(a)]^(2))/(2)`

D

`([g(b)]^(2)-[g(a)]^(2))/(2)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. T h ev a l u eofint0^(pi/2)(dx)/(1+tan^3x)i s 0 (b) 1 (c) pi/2 (d...

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  2. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >...

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  3. If (d(f(x)))/(dx) = g(x) AA x in [a, b] then int(a)^(b)f(x).g(x)dx is ...

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  4. For any integer n,the integral overset(pi)underset(0)int e^(sin^(2)x)c...

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  5. The value of the integral int(0)^(3) sqrt(3+x^(3))dxlies in the inter...

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  6. The value of the integral int(0)^(1) (1)/((1+x^(2))^(3//2))dx is

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  7. If I = int(0)^(2pi)sin^(2)xdx, then

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  8. If int(0)^(1) f(x)=M,int(0)^(1) g(x)dx=N, then which of the following ...

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  9. The value of int( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

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  10. The value of int(-pi//2)^(pi//2) sin{log(x+sqrt(x^(2)+1)}dx is

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  11. The value of int(0)^(2pi) cos^(99)x dx, is

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  12. If f(a+x)=f(x), then int(0)^(na) f(x)dx is equal to (n in N)

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  13. If f(t) is an odd function, then prove that varphi(x)=inta^xf(t)dt is ...

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  14. If f(x) is an integrable function over every interval on the real line...

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  15. If I(1)=int(3pi)^(0) f(cos^(2)x)dx and I(2)=int(pi)^(0) f(cos^(2)x) th...

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  16. If f(x) is a quadratic polynomial in x such that 6int0^1 f(x)dx-{f(0...

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  17. The value of integral int(-2)^(4) x[x]dx is

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  18. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

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  19. Given that, F(x)=(1)/(x^(2))int(4)^(x)(4t^(2)-2F'(t))dt, find F'(4).

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  20. It is known that f(x) is an odd function in the interval [p/2, p/2] an...

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