Description : `int (dx)/(x(1+log_(e)x)(3+log_(e)x))`
Last Answer : `int (dx)/(x(1+log_(e)x)(3+log_(e)x))`
Description : `int(1)/(x cos^(2)(log_(e)x))dx`
Last Answer : `int(1)/(x cos^(2)(log_(e)x))dx`
Description : `int_(-1)^(2) e^(-x)dx`
Last Answer : `int_(-1)^(2) e^(-x)dx`
Description : `int_(0)^(2) e^(x) dx`
Last Answer : `int_(0)^(2) e^(x) dx`
Description : `int_(0)^(pi//2) e^(x) (sin x + cos x) dx`
Last Answer : `int_(0)^(pi//2) e^(x) (sin x + cos x) dx`
Description : `int_(0)^(pi//4) e^(x) (tan x+ sec^(2)x) dx`
Last Answer : `int_(0)^(pi//4) e^(x) (tan x+ sec^(2)x) dx`
Description : `int_(0)^(2) (e^(-1//x))/(x^(2)) dx`
Last Answer : `int_(0)^(2) (e^(-1//x))/(x^(2)) dx`
Description : `(i) int_(0)^(pi//4) e^(tanx) . sec^(2) x dx` `(ii) int_(0)^(pi//4) (sin (cos 2x))/(" cosec " 2x)dx`
Last Answer : `(i) int_(0)^(pi//4) e^(tanx) . sec^(2) x dx` `(ii) int_(0)^(pi//4) (sin (cos 2x))/(" cosec " 2x)dx`
Description : `int_(0)^(1) (1)/(e^(x) +e^(-x)) dx`
Last Answer : `int_(0)^(1) (1)/(e^(x) +e^(-x)) dx`
Description : `int_(1)^(e) (e^(x) (1+xlog x))/(x) dx`
Last Answer : `int_(1)^(e) (e^(x) (1+xlog x))/(x) dx`
Description : `int_(0)^(pi//2) " cosec "(x-(pi)/(3)) " cosec "(x-(pi)/(6)) dx=?`
Last Answer : `int_(0)^(pi//2) " cosec "(x-(pi)/(3)) " cosec "(x-(pi)/(6)) dx=?` A. `-log 3` B. `-2 log 3` C. `2 log 3` D.
Description : `int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?`
Last Answer : `int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?` A. `0` B. `1` C. None of the above D.
Description : `int_(0)^(1) cot^(-1) (1-x+x^(2)) dx=?`
Last Answer : `int_(0)^(1) cot^(-1) (1-x+x^(2)) dx=?` A. `(pi)/(2) +log 2` B. `(pi)/(2) -log 2` C. `-(pi)/(2) - log 2` D.
Description : `int_(0)^(pi) sin (n+(1)/(2))x. " cosec ".(x)/(2) dx=?`
Last Answer : `int_(0)^(pi) sin (n+(1)/(2))x. " cosec ".(x)/(2) dx=?` A. `(pi)/(2)` B. `pi` C. `2pi` D.
Description : `int_(0)^(pi//4) sqrt(cot x dx) =?`
Last Answer : `int_(0)^(pi//4) sqrt(cot x dx) =?` A. `(Pi sqrt(2))/(4)+(1)/(sqrt(2)) log (sqrt(2)-1)` B. `(- ... (pisqrt(2))/(4) -(1)/(sqrt(2))log (sqrt(2)-1)` D.
Description : `int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=?`
Last Answer : `int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=?` A. `(pi sqrt(3))/(12)+(1)/(2)` B. `(pisqrt(3))/(12)-(1)/(2)` C. `(pisqrt(3))/(12) -(1)/(2)` D.
Description : `" if " f(x) ={ underset( 5x" "2 le x le 3) (3x+ 4,0 le x le 2),` then `int_(0)^(3) f(x) dx=?`
Last Answer : `" if " f(x) ={ underset( 5x" "2 le x le 3) (3x+ 4,0 le x le 2),` then `int_(0)^(3) f(x) dx=?` A. `(53)/(2)` B. `(55)/(2)` C. `(57)/(2)` D.
Description : `int_(0)^(pi//4) log (1+tan x) dx =?`
Last Answer : `int_(0)^(pi//4) log (1+tan x) dx =?` A. `(pi)/(4) log 2` B. `(pi)/(6) log 2` C. `(pi)/(8) log 2` D.
Description : `int_(0)^(pi//2) x sin cos x dx=?`
Last Answer : `int_(0)^(pi//2) x sin cos x dx=?` A. `(pi)/(4)` B. `(pi)/(8)` C. `(pi)/(12)` D.
Description : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx=?`
Last Answer : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx=?` A. `sqrt(2)-1` B. `sqrt(2)` C. `-sqrt(2)` D.
Description : `int_(0)^(1) sqrt((1-x)/(1+x)) dx=?`
Last Answer : `int_(0)^(1) sqrt((1-x)/(1+x)) dx=?` A. `(pi)/(2)+1` B. `(pi)/(2) -1` C. None of these D.
Description : `int_(0)^(1) x (1 -x)^(n) dx=?`
Last Answer : `int_(0)^(1) x (1 -x)^(n) dx=?` A. `(1)/((n+1)(n+2))` B. `(1)/(n(n+2))` C. `(1)/((n+1)(n+3))` D.
Description : `int_(2)^(8) |x-5| dx=?`
Last Answer : `int_(2)^(8) |x-5| dx=?` A. 9 B. 10 C. 11 D.
Description : `int_(-4)^(4) log ((7-x )/(2+x)) dx=?`
Last Answer : `int_(-4)^(4) log ((7-x )/(2+x)) dx=?` A. 4 B. -4 C. 0 D. 1
Description : `int_(-2)^(2) X sin^(10) x dx =?`
Last Answer : `int_(-2)^(2) X sin^(10) x dx =?` A. `-2` B. 4 C. None of the above D.
Description : `int_(1)^(5) (x^(2) -2x) dx`
Last Answer : `int_(1)^(5) (x^(2) -2x) dx`
Description : `int_(0)^(3)(x^(2)+1)dx`
Last Answer : `int_(0)^(3)(x^(2)+1)dx`
Description : `int_(2)^(4) x dx`
Last Answer : `int_(2)^(4) x dx`
Description : `"if "f(x) ={ underset(5x, 1,2 le x le 3)(3x+4, 0 le x le 2}},` then evaluate `int_(0)^(3) f(x) dx.`
Last Answer : `"if "f(x) ={ underset(5x, 1,2 le x le 3)(3x+4, 0 le x le 2}},` then evaluate `int_(0)^(3) f(x) dx.`
Description : Evaluate : `int_(0)^(1) (1-x)^(3//2) dx`
Last Answer : Evaluate : `int_(0)^(1) (1-x)^(3//2) dx`
Description : `int_(0)^(pi) x sin x. cos^(2) x dx`
Last Answer : `int_(0)^(pi) x sin x. cos^(2) x dx`
Description : `int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx`
Last Answer : `int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx`
Description : `int_(0)^(pi//2) (dx)/(1+2 cos x)`
Last Answer : `int_(0)^(pi//2) (dx)/(1+2 cos x)`
Description : `int_(0)^(pi//2) x sin x cos x dx`
Last Answer : `int_(0)^(pi//2) x sin x cos x dx`
Description : `int_(0)^(2) sqrt((2+x)/(2-x)) dx`
Last Answer : `int_(0)^(2) sqrt((2+x)/(2-x)) dx`
Description : `int_(a)^(b)cos x dx`
Last Answer : `int_(a)^(b)cos x dx`
Description : `int_(a)^(b) sin x dx`
Last Answer : `int_(a)^(b) sin x dx`
Description : `"If "f(x) ={underset(x^(2)+1.2 le x le 3)(2x+1.1 le x le 2),` then evaluate `int_(1)^(3) f(x) dx.`
Last Answer : `"If "f(x) ={underset(x^(2)+1.2 le x le 3)(2x+1.1 le x le 2),` then evaluate `int_(1)^(3) f(x) dx.`
Description : Evaluate :`int_(-pi//4)^(pi//4) |sin x|dx`
Last Answer : Evaluate :`int_(-pi//4)^(pi//4) |sin x|dx`
Description : Evaluate :`int_(0)^(8) |x-5|dx`
Last Answer : Evaluate :`int_(0)^(8) |x-5|dx`
Description : Evaluate :` int_(-pi//2)^(pi//2) |sin x|dx`
Last Answer : Evaluate :` int_(-pi//2)^(pi//2) |sin x|dx`
Description : Evaluate : `int_(0)^(4) x(4-x)^(3//2)dx`
Last Answer : Evaluate : `int_(0)^(4) x(4-x)^(3//2)dx`
Description : `int_(0)^(pi) x sin^(2) x dx`
Last Answer : `int_(0)^(pi) x sin^(2) x dx`
Description : `int_(0)^(pi) (1-x^(2))/((1+x^(2))^(2))dx`
Last Answer : `int_(0)^(pi) (1-x^(2))/((1+x^(2))^(2))dx`
Description : `int_(0)^(pi) (1)/(5+2 cos x)dx`
Last Answer : `int_(0)^(pi) (1)/(5+2 cos x)dx`
Description : `int_(1)^(2) (1)/(2(1+x^(4)))dx`
Last Answer : `int_(1)^(2) (1)/(2(1+x^(4)))dx`
Description : `int_(0)^(pi//2) (1)/(4+3 cos x)dx`
Last Answer : `int_(0)^(pi//2) (1)/(4+3 cos x)dx`
Description : `int_(0)^(1) (1)/(x^(2) +2x+3)dx`
Last Answer : `int_(0)^(1) (1)/(x^(2) +2x+3)dx`
Description : `int_(0)^(1//sqrt(2)) (sin^(-1))/((1-x^(2))^(3//2))dx`
Last Answer : `int_(0)^(1//sqrt(2)) (sin^(-1))/((1-x^(2))^(3//2))dx`