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//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 : `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)/(5+2 cos x)dx`
Last Answer : `int_(0)^(pi) (1)/(5+2 cos x)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)^(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//6) cos x cos 3x dx`
Last Answer : ` int_(0)^(pi//6) cos x cos 3x 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 : `(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)^(pi//2) x^(2) cos x dx`
Last Answer : `int_(0)^(pi//2) x^(2) cos x dx`
Description : `int_(pi//6)^(pi//2) cos x dx`
Last Answer : `int_(pi//6)^(pi//2) cos x dx`
Description : The value of definite integral `int_(-pi)^(pi) (cos 2x. cos2^(2)x.cos2^(3)x.cos 2^(4)x.cos2^(5)x)dx` is
Last Answer : The value of definite integral `int_(-pi)^(pi) (cos 2x. cos2^(2)x.cos2^(3)x.cos 2^(4)x.cos2^(5)x)dx` is A. 1 B. `-1` C. 0 D. 2
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//2) sqrt(1- cos 2x) dx`
Last Answer : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Description : `int_(0)^(pi//2) cos 3x dx`
Last Answer : `int_(0)^(pi//2) cos 3x dx`
Description : \( Q: \int_{\frac{5 \pi}{4}}^{\frac{3 \pi}{2}} \frac{\frac{x}{x}-\frac{x \cdot x}{2}+\frac{(x 2)^{2}}{24}-\frac{x^{4} x 2}{720}+\cdots \infty}{\sqrt{\frac{1-\cos 2 x}{8}}} \)
Last Answer : (a) \( \infinite \) (b) \( \ln 2 \) (C) 0 (d) \( -2 \ln \sqrt{2} \) (e) \( e^{2} \)
Description : `int_(0)^(pi//4) cos 0. " cosec"^(2) 0 do`
Last Answer : `int_(0)^(pi//4) cos 0. " cosec"^(2) 0 do`
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) 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//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) 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//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) sin^(2) x dx`
Last Answer : `int_(0)^(pi//2) sin^(2) 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//4) sin ^(2) x dx`
Last Answer : `int_(0)^(pi//4) sin ^(2) x dx`
Description : `int_(0)^(pi//4) tan x dx`
Last Answer : `int_(0)^(pi//4) tan x dx`
Description : `int_(a)^(b)cos x dx`
Last Answer : `int_(a)^(b)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_(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_(-pi//4)^(pi//4) "cosec"^(2) x dx`
Last Answer : `int_(-pi//4)^(pi//4) "cosec"^(2) x dx`
Description : `int_(0)^(pi) sin 3x dx`
Last Answer : `int_(0)^(pi) sin 3x dx`
Description : `int_(0)^(pi//6) sqrt(1-sin 2x) dx`
Last Answer : `int_(0)^(pi//6) sqrt(1-sin 2x) dx`
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)^(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)^(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_(0)^(2) e^(x) dx`
Last Answer : `int_(0)^(2) e^(x) dx`
Description : `int_(0)^(3)(x^(2)+1)dx`
Last Answer : `int_(0)^(3)(x^(2)+1)dx`