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Let f(x) = {:[(e^(cos x) sinx",", "for" ...

Let `f(x) = {:[(e^(cos x) sinx",", "for" |x| le 2),(2,"otherwise"):}` then : `int_(-2)^(3) f(x) dx` = …………….

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MODERN PUBLICATION-DEFINITE INTEGRALS-MULTIPLE CHOICE QUESTIONS (LEVEL - II)
  1. int0^1 |sin 2 pi x| dx is equal to :

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  2. If f(x) = f(a - x), then int0^(a) xf(x) dx is equal to :

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  3. Let f(x) = {:[(e^(cos x) sinx",", "for" |x| le 2),(2,"otherwise"):} th...

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  4. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

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  5. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

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  6. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  7. If (1 sin t)/(1 + t) dt = alpha, then that value of the integral : i...

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  8. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

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  9. Let f(x) = int1^x sqrt(2 - t^2)dt. Then the real roots of the equation...

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  10. Let T > 0 be a fixed real number. Suppose f is a continuous function s...

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  11. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

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  12. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

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  13. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

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  14. If f(x) = int(x^2)^(x^2 + 1) e^(-t^2) dt, find the interval in which f...

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  15. If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-a))^(f(a)) x g {x(1 - x)} dx a...

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  16. The value of the integral int0^1 sqrt((1 - x)/(1 + x))dx is :

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  17. If I(1) = int0^(1) 2^(x^(2)) dx, I(2) = int0^(1) 2^(x^(3)) dx, I(3) = ...

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  18. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

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  19. lim(n to oo) [1/(n^2) "sec"^2 1/(n^2) + 2/(n^2) "sec"^(2) 4/(n^2) + ……...

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  20. Let F(x) = f(x) + f(1/x), where , f(x) = int1^x (log t)/(1 + t) dt. Th...

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