59. letfbe an integrable function over [a, b] and m be the upper bound of fin [a, b], then: (a)f d2 m(b- a) (b)fdx = m(b - a) (c)fdr s m (b - a) (d) none of the

59. Letfbe an integrable function over [a, b] and M be the upper bound of fin [a, b], then: (A)f d2 M(b- a) (B)fdx = M(b - a) (C)fdr s M (b - a) (D) None of these 60. Let P be a partition of [a, b], M be the upper bound of f in la, b], U (P.) be the upper sum off to the partition P. Then : (A) M (b-a) 2 U (p, (B) M(b-a)=U(p,1) (C) M (b- a) < U (p, N (D) None of these 61. If f, and fy are both differentiable at a point (a, b), then by Young's theorem (A) Sy(a,b) = Sa(a, b) (B) S5a,b) = -Sx(a, b) (C) Sya,b) S(a, b) (D) None of these 62. If a series 2Jn converges uniformly to f on [a, b] and each term J,(x) is integrable on [a, b], then: (A) d = -En , drVxe la, b] (B) Jsd ,U,a) Vx e [a, b] VxE la,b] (D) None of these 63. A bounded function, having a finite number of points of discontinuity on [a, b], is on [a, b]. (A) integrable (B) not integrable (C) differentiable (D) None of these (15) XE(H-3)-MAT(5)