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Property 6: If f(x) is a continuous func...

Property 6: If f(x) is a continuous function defined on `[0; 2a]` then ` int_0 ^2a = int_0 ^a f(x) dx + int_0 ^a f(2a - x) dx`

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Property 6: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx

Property 5: If f(x) is a continuous function defined on [0;a] then int_(0)^(a)f(x)dx=int_(0)f(a-x)dx

Property 10: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=2int_(0)^(a)f(x)dx if f(2a-x)=f(x) and 0 if f(2a-x)=-f(x)

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

int_0^a f(a-x) dx=

Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even

Property 8: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=int_(0)^(a){f(x)+f(-x)}dx

Property 7: Let f(x) be a continuous function of x defined on [0;a] such that f(a-x)=f(x) then int_(0)^(a)xf(x)dx=(a)/(2)int_(0)^(a)f(x)dx

int _(0) ^(2a) f (x) dx = int _(0) ^(a) f (x) dx + int _(0)^(a) f (2a -x ) dx

int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=

GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2014-SECTION-II
  1. If y=1-costheta,x=1-sintheta,"then "(dy)/(dx)" at "theta=(pi)/(4)" is"

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  2. The integrating factor of linear differential equation (dy)/(dx) + y s...

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  3. Find the equation of the tangent to the curve y=3x^(2)-x+1 at P(1, 3).

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  4. Examine the continuity of the funciton f(x)=sinx - cos x, " for "x n...

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  5. Verify Rolle's theorem for the following function f(x) = x^2 - 5x + 9,...

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  6. intsec^nxtanxdx,n!=0

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  7. The probability mass function (p. m. f.) of X is given below : |{:(X...

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  8. Given that X ~ B( n=10, p) .If E (x) = 8, find the value of p .

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  9. If y =f(u) is differentiable function of u, and u=g(x) is a differenti...

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  10. Obtion the differential equation by elininating arbitrary constants A,...

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  11. Evaluate int(x^2+1)/((x^2+2)(2x^2+1))dx

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  12. An open box is to be made out of a piece of a square card board of sid...

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  13. Property 6: If f(x) is a continuous function defined on [0; 2a] then ...

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  14. If the function f(x) is continuous in the interval [-2, 2]. find the ...

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  15. Solve the following differential equations : (1) (dy)/(dx) = (y + s...

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  16. A fiar coin is tossed 18 times. Find the probability that it shows lea...

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  17. If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?

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  18. Find the area bounded by the cirxle x^2+y^2 =16 and the line y=x in th...

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  19. int sqrt(x^2 - a^2) = 1/2 x sqrt (x^2 - a^2) - 1/2 a^2 log ( x + sqrt(...

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  20. A random variable X has the following probability distribution : (a...

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