Let y= {x}^([x]) then the value of int...

Let `y= {x}^([x])` then the value of `int_0^3 yd x` equals to (where {.} and [.] denote fractional part and integerpart function respectively)

`11/6`

`5/6`

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VIKAS GUPTA (BLACK BOOK) ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Let y= {x}^([x]) then the value of int0^3 yd x equals to (where {.} ...
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int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...
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If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...
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Let f (x) = x cos x, x in [(3pi)/(2), 2pi] and g (x) be its inverse. ...
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If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...
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If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(s...
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The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...
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Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...
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Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2)+1))")")dx...
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If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...
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Find the value of |a| for which the area of triangle included between ...
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Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...
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If I = int (0) ^(100) (sqrtx)dx, then the value of (9I)/(155) is:
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Let I(n) = int (0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx where ...
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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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underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...
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The maximum value of int (-pi//2) ^(2pi//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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