Description : Evaluate `int_0^(pi/4)(sqrt(tanx)+sqrt(cotx))dx`
Last Answer : Evaluate `int_0^(pi/4)(sqrt(tanx)+sqrt(cotx))dx` A. `-(pi)/(sqrt(2))` B. `(pi)/(2)` C. `-(pi)/(2)` D.
Description : Evaluate : `int_(pi/3)^(pi/4)(tanx+cotx)^2dx`
Last Answer : Evaluate : `int_(pi/3)^(pi/4)(tanx+cotx)^2dx`
Description : Evaluate: `int(sqrt(tanx)+sqrt(cotx))dx`
Last Answer : Evaluate: `int(sqrt(tanx)+sqrt(cotx))dx`
Description : Evaluate: (i) `intsecxlog(secx+tanx) dx` (ii) `intcos e c xlog(cos e c x-cotx) dx`
Last Answer : Evaluate: (i) `intsecxlog(secx+tanx) dx` (ii) `intcos e c xlog(cos e c x-cotx) dx`
Description : prove that `int_0^oo x^2/((x^2+a^2)(x^2+b^2))dx=pi/(2(a+b))`
Last Answer : prove that `int_0^oo x^2/((x^2+a^2)(x^2+b^2))dx=pi/(2(a+b))`
Description : Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx`
Last Answer : Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx` A. `(pi(a^(2) +b^(2)))/(4a^(3)b^(3))` B. ` ... )+b^(2)))/(4a^(2)b^(2))` C. None of the above D.
Description : integrate `int_0^(2pi) e^x . sin (pi/4 + x/2) dx`
Last Answer : integrate `int_0^(2pi) e^x . sin (pi/4 + 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(cotx)/(log(sinx)dx`
Last Answer : `int(cotx)/(log(sinx)dx`
Description : The minimum distance between the curves `y=tanx, AA x in (-(pi)/(2),(pi)/(2)) and (x-2-(pi)/(4))^(2)+y^(2)=1` is
Last Answer : The minimum distance between the curves `y=tanx, AA x in (-(pi)/(2),(pi)/(2)) and (x-2-(pi)/(4))^(2)+y^(2 ... )-1` B. `sqrt(5)+1` C. `sqrt(2)-1` D. 2`
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 : `(i) int_(0)^(pi//2) x cos x dx` (i) `int_(1)^(3) x. log x dx`
Last Answer : `(i) int_(0)^(pi//2) x cos x dx` (i) `int_(1)^(3) x. log x dx`
Description : `int_0^a(dx)/(sqrt(a x-x^2))`
Last Answer : `int_0^a(dx)/(sqrt(a x-x^2))`
Description : `intsqrt(cotx) dx`
Last Answer : `intsqrt(cotx) dx`
Description : `int(sec^(2)x)/(sqrt(tanx))dx`
Last Answer : `int(sec^(2)x)/(sqrt(tanx))dx`
Description : `int1/(cos^2x(1-tanx)^2) dx`
Last Answer : `int1/(cos^2x(1-tanx)^2) dx`
Description : Evaluate : `int_0^1x(1-x)^5dx`
Last Answer : Evaluate : `int_0^1x(1-x)^5dx`
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)^(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)^(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)^(pi) x sin x. cos^(2) x dx`
Last Answer : `int_(0)^(pi) x sin x. cos^(2) x 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 : Evaluate :`int_(-pi//4)^(pi//4) |sin x|dx`
Last Answer : Evaluate :`int_(-pi//4)^(pi//4) |sin x|dx`
Description : Evaluate :` int_(-pi//2)^(pi//2) |sin x|dx`
Last Answer : Evaluate :` int_(-pi//2)^(pi//2) |sin x|dx`
Description : `int_(0)^(pi) x sin^(2) x dx`
Last Answer : `int_(0)^(pi) x sin^(2) 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) (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_(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)^(pi//2) (1)/(4+3 cos x)dx`
Last Answer : `int_(0)^(pi//2) (1)/(4+3 cos x)dx`
Description : `int_(pi//6)^(pi//2) (" cosec x cot x")/(1+" cosec "^(2) x)dx`
Last Answer : `int_(pi//6)^(pi//2) (" cosec x cot x")/(1+" cosec "^(2) x)dx`
Description : `int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)`
Last Answer : `int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)`
Description : `int_(0)^(pi//2) sin^(2) x cos ^(2) x dx`
Last Answer : `int_(0)^(pi//2) sin^(2) x cos ^(2) x dx`
Description : `int_(0)^(pi//2) (a cos^(2) x+b sin^(2) x) dx`
Last Answer : `int_(0)^(pi//2) (a cos^(2) x+b sin^(2) x) dx`
Description : `int_(0)^(pi//4) (1)/(1+cos 2x)dx`
Last Answer : `int_(0)^(pi//4) (1)/(1+cos 2x)dx`
Description : ` int_(0)^(pi//6) cos x cos 3x dx`
Last Answer : ` int_(0)^(pi//6) cos x cos 3x dx`
Description : `int_(0)^(pi//2) sin^(2) x dx`
Last Answer : `int_(0)^(pi//2) sin^(2) x dx`
Description : `(i) int_(0)^(pi//2) x sin x cos x dx` `(ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx`
Last Answer : `(i) int_(0)^(pi//2) x sin x cos x dx` `(ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx`
Description : `int_(0)^(pi//2) x^(2) cos x dx`
Last Answer : `int_(0)^(pi//2) x^(2) cos x dx`
Description : `int_(0)^(pi//2) sin ^(4) x dx`
Last Answer : `int_(0)^(pi//2) sin ^(4) x dx`
Description : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Last Answer : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Description : `int_(0)^(pi//4) sin ^(2) x dx`
Last Answer : `int_(0)^(pi//4) sin ^(2) x dx`
Description : `int_(0)^(pi//2) cos 3x dx`
Last Answer : `int_(0)^(pi//2) cos 3x dx`
Description : `int_(-pi//4)^(pi//4) "cosec"^(2) x dx`
Last Answer : `int_(-pi//4)^(pi//4) "cosec"^(2) x dx`
Description : `int_(pi//6)^(pi//2) cos x dx`
Last Answer : `int_(pi//6)^(pi//2) cos x dx`