Archives

∫x log x dx =

1) (x2 / 4) [2 log x - 1] + c 2) (x2 / 2) [2 log x - 1] + c 3) (x2 / 4) [2 log x + 1] + c 4) (x2 / 2) [2 log x + 1] + c Solution: (1) (x2 /... View Article

∫[(1 + x⁴) / (1 – x⁴)^3/2] dx =

1) [x / √1 - x4] + c 2) [- x / √1 - x4] + c 3) [2x / √1 - x4] + c 4) [- 2x / √1 - x4] + c Solution: (1) [x / √1 - x4] + c... View Article

If ∫uv’’ dx = uv’ – vu’ + a, then a =

1) ∫uv’’ dx 2) ∫u’v dx 3) ∫uv’ dx 4) ∫u’’ dx Solution: (1) ∫uv’’ dx ∫uv’’ dx = uv’ - ∫u’v’ dx = uv’ - uv + ∫u’’v dx... View Article

If ∫[(x² – 2) / (x³ √x² – 1))] dx =

1) [(x2) / √x2 - 1)] + c 2) [(- x2) / √x2 - 1)] + c 3) [(√x2 - 1) / (x2)] + c 4) [- (√x2 - 1) / (x2)] + c Solution: (4) [- (√x2 - 1) / (x2)] + c... View Article

If ∫dx / [x⁴ + x³] = [A / x²] + (B / x) + log |x / (x + 1)| + c, then

1) A = 1/2, B = 1 2) A = 1, B = 1/2 3) A = - (1/2) , B = 1 4) A = 1, B = 1 Solution: (3) A = - (1/2) , B = 1... View Article

If ∫[log (log x) + 1 / (log x)²] dx = x [f (x) – g (x)] + c

1) f (x) = log (log x); g (x) = 1 / log x 2) f (x) = log x, g (x) = 1 / log x 3) f (x) = 1 / [x log x]; g (x) = log (log x) 4) f (x) = 1 / [x... View Article

If l_n = ∫sinⁿ x dx, then nl_n – (n – 1) l_n-2 =

1) sinn-1 x cos x 2) cosn-1 x sin x 3) - sinn-1 x cos x 4) - cosn-1 x sin x Solution: (3) - sinn-1 x cos x... View Article

∫[log (x + √1 + x²) / √1 + x²] dx =

1) [log (x + √1 + x2)]2 + c 2) x log (x + √1 + x2) + c 3) (1 / 2) log (x + √1 + x2) + c 4) (1 / 2) [log (x + √1 + x2)]2 + c 5) (x / 2) log (x... View Article

If ∫[(x + 2) / (2x² + 6x + 5)] dx = P ∫[(4x + 6) / (2x² + 6x + 5)] dx + (1 / 2) ∫dx / (2x² + 6x + 5), then the value of P is

1) 1/3 2) 1/2 3) 1/4 4) 2 5) 1 Solution: (3) ¼... View Article

∫[dx / (√1 – e^2x)] =

∫[(cos x + x sin x) / (x² + x cos x)] dx =

∫[(1 + x) / (x + e^-x)] dx =

1) log |(x - e-x)| + c 2) log |(x + e-x)| + c 3) log |(1 + xex)| + c 4) (1 + xe-x)2 + c 5) log |(1 - xex)| + c Solution: (3) log |(1 + xex)|... View Article

∫[(x² + 1) √(x + 1)] dx =

1) 2) 3) 4) 5) Solution: (2)... View Article

∫e^x [(2 / x) – (2 / x²) dx] =

1) (ex / x) + c 2) (ex / 2x2) + c 3) (2ex / x) + c 4) (2ex / x2) + c Solution: (3) (2ex / x) + c ∫ex [(2 / x) - (2 / x2) dx] = 2 ∫[ex (x -... View Article

∫{log √x / (3x)} dx =

1) (1 / 3) (log √x)2 + c 2) (2 / 3) (log √x)2 + c 3) (2 / 3) (log x)2 + c 4) (1 / 3) (log x)2 + c Solution: (1) (1 / 3) (log √x)2 + c ∫{log... View Article

25 May 2021: PIB Summary & Analysis

May 25th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. Vesak or Buddha Purnima 2. National Mission on use of Biomass in Thermal Power... View Article

Mayflower 400 – World’s First Artificial Intelligence Ship

The Mayflower 400 is the world’s first artificial intelligence managed vessel to sail on a transatlantic voyage. It will track aquatic mammals,... View Article

M	T	W	T	F	S	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31