PYQSide
ExamsMy practice
The value of - /6 /6 ( + 4x111 - (|x| + /6) )dx is equal to:
(2) 4
The denominator is an even function of x, so 4x111 - (|x| + /6) is odd and its integral over [- /6, /6] is 0.
I = - /6 /6 1 - (|x| + /6)dx = 2 0 /6 dx1 - (x + /6)
Put x + /6 = t: I = 2 /6 /3 dt1 - t
= 2 /6 /3 1 + t 2 tdt = 2 /6 /3( 2 t + t t) dt
= 2 [ t + t ] /6 /3
= 2 [( 3 + 2) - ( 1 3 + 2 3 ) ]
= 2 [( 3 + 2) - 3] = 4
Answer: (2)
6 0 |( 3x + 2x + x)| dx is equal to .
Let [ ] denote the greatest integer function and f(x) = n 1n3 k=1n [ k23x ]. Then 12 j=1 f(j) is equal to .
If 01 4 -1 (1 - 2x + 4x2 )dx = a -1(2) - b e(5), where a, b N, then (2a + b) is equal to .
The integral -1 32 ( | 2 x ( x) | )dx is equal to:
Let f(x) be a positive function and I1 = - 121 2x f(2x(1 - 2x)) dx and I2 = -12 f(x(1 - x)) dx. Then the value of I2I1 is equal to
The integral 0 (x+3) x1+3 2 x dx is equal to
If ( 1x + 1x3 ) ( [23]3x-24 + x-26 ) dx = - 3( + 1) (3x + x ) + 1 + C, x > 0, ( , , Z), where C is the constant of integration, then + + is equal to .
The value of -11 (1 + |x| - x ) ex + ( |x| - x ) e-xex + e-x dx is equal to
Let f(x)+2f ( 1x )=x2+5 and 2g(x)-3g ( 12 )=x, x>0. If = 12 f(x) dx, and = 12 g(x) dx, then the value of 9 + is :
If ( 1+x2+x )10 ( 1+x2-x )9 dx= 1m ( ( 1+x2+x )n (n 1+x2-x ) )+C where C is the constant of integration and m, n N, then m+n is equal to .