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[21]Quest Tutorials North Delhi : E-16/289, Sector-8, Rohini, New Delhi. Ph. 65395439 Quest Q.150 The value of the definite integral, ∫ π 2 0 dx xsin x5sin is (A) 0 (B) 2 π (C) π (D) 2π Select the correct alternatives : (More than one are correct) Q.151 dxxsgn b a ∫ = (where a, b∈ R) (A) | b | – | a | (B) (b–a) sgn (b–a) (C) b sgnb – a sgna (D) | a | – | b | Q.152 ∫ + xcos45 dx = λ tan−1 2 x tanm + C then : (A) λ = 2/3 (B) m = 1/3 (C) λ = 1/3 (D) m = 2/3 Q.153 Which of the following are true ? (A) x f x a a . (sin ) π − ∫ dx = π 2 . f x a a (s in ) π − ∫ dx (B) f x a a ( )2 − ∫ dx = 2. f x a ( )2 0 ∫ dx (C) ( )f x n cos 2 0 π ∫ dx = n. ( )f xcos2 0 π ∫ dx (D) f x c b c ( )+ − ∫ 0 dx = f x c b ( )∫ dx Q.154 The value of ( ) 2 3 3 1 2 2 2 2 0 1 x x x x x + + + + +∫ ( ) dx is : (A) π 4 + 2 ln2 − tan−1 2 (B) π 4 + 2 ln2 − tan−1 1 3 (C) 2 ln2 − cot−1 3 (D) − π 4 + ln4 + cot−1 2 Q.155 x x x 2 2 21 + +∫ cos cosec2 x dx is equal to : (A) cot x − cot −1 x + c (B) c − cot x + cot −1 x (C) − tan −1 x − cos sec ec x x + c (D) − e n x� tan−1 − cot x + c where 'c' is constant of integration . Q.156 Let f (x) = sin t t x 0 ∫ dt (x > 0) then f (x) has : (A) Maxima if x = n π where n = 1, 3, 5,..... (B) Minima if x = n π where n = 2, 4, 6,...... (C) Maxima if x = n π where n = 2, 4, 6,...... (D) The function is monotonic
