Statement 1: For −1<a<4,∫x2+2(a−1)x+a+5dx =λlog∣g(x)∣+c, where λandc are constants Statement 2: For −1<a<4,x2+2(a−1)x+a+51iscont∈uouunction
If f(x)=∫x4−2x2+2x8+4dx and f(0)=0,then (a)f(x) is an odd function (b)f(x) has range R (c)f(x) has at least one real root (d)f(x) is a monotonic function.
A curve g(x)=∫x27(1+x+x2)6(6x2+5x+4)dx is passing through origin. Then g(1)=737 (b) g(1)=727 g(−1)=71 (d) g(−1)=1437
If∫4ex+5e−x3ex−5e−1dx=ax+bln(4ex+5e−x)+C,then a=−81,b=87 (b) a=81,b=87 a=−81,b=−87 (d) a=81,b=−87
If lprime(x) means logloglogx, the log being repeated r times, then ∫[xl(x)l2(x)l3(x)lprime(x)]−1ds is equal to lr+1(x)+C (b) r+1lr+1(x)+C lr(x)+C (d) none of these
Each question has four choices, a,b,c and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. If both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1. If both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1. If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE. If STATEMENT 1 is FALSE and STATEMENT 2 is TRUE. Statement 1: ∫exsinxdx=2ex(sinx−cosx)+c Statement 2: ∫ex(f(x)+fprime(x))dx=exf(x)+c