Let l (n) =int (-1) ^(1) |x|(1+ x+ (x ^(...

Let `l _(n) =int _(-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(2))/(3) + ..... + (x ^(2n))/(2n))dx if lim _(x to oo) l _(n) ` can be expressed as rational `p/q` in this lowest form, then find the value of `(pq(p+q))/(10)`

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Let l _(n) =int _(-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(3))/(3) + ..... + (x ^(2n))/(2n))dx if lim _(x to oo) l _(n) can be expressed as rational p/q in this lowest form, then find the value of (pq(p+q))/(10)

Let I_n=int_- 1^1|x|(1+x+(x^2)/2+(x^3)/3+.....+(x^(2n))/(2n))dx where n in N . If lim_(n->oo) I_n can be expressed as a ration number p/q in the lowest form, then find the value of p + q

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If the value of the sum n^(2) + n - sum_(k = 1)^(n) (2k^(3)+ 8k^(2) + 6k - 1)/(k^(2) + 4k + 3) as n tends to infinity can be expressed in the form (p)/(q) find the least value of (p + q) where p, q in N

VK JAISWAL ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Find the value of |a| for which the area of triangle included between ...
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int( x^3)/(x^2-3)dx
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If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...
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int( x^3)/(x^2-2)dx
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If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...
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Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...
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Find the vlaur of lim (n to oo) (1)/(sqrtn)(1+ (1)/(sqrt2) +(1)/(sqrt3...
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The maximum value of int (-pi/2) ^((3pi)/2) sin x. f (x) dx, subject t...
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Given a function g, continous everywhere such that g (1)=5 and int (0)...
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If f (n)= 1/pi int (0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2)...
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Let f (2-x) =f (2+xand f (4-x )= f (4+x). Function f (x) satisfies int...
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Let l (n) =int (-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(2))/(3) + ........
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int sqrt (x^2+4) dx
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If int (a )^(b) |sin x |dx =8 and int (0)^(a+b) |cos x| dx=9 then the ...
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If f(x),g(x),h(x) and phi(x) are polynomial in x, (int1^x f(x) h(x) dx...
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If int (0)^(2)(3x ^(2) -3x +1) cos (x ^(3) -3x ^(2)+4x -2) dx = a sin ...
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let f (x) = int (0) ^(x) e ^(x-y) f'(y) dy - (x ^(2) -x+1)e ^(x) Fin...
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For a positive integer n, let I (n) int (-pi)^(pi) ((pi)/(2) -|x|) cos...
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