Description : `int_(0)^(pi//6) sqrt(1-sin 2x) dx`
Last Answer : `int_(0)^(pi//6) sqrt(1-sin 2x) dx`
Description : If the function `f(x) = a sin x + 1/3 sin 3x ` is maximum at `x= pi/3 ` a=?
Last Answer : If the function `f(x) = a sin x + 1/3 sin 3x ` is maximum at `x= pi/3 ` a=? A. 1 B. 2 C. 3 D. 4
Description : Find the maximum and minimum values of the function `f(x) = x+ sin 2x, (0 lt x lt pi)`.
Last Answer : Find the maximum and minimum values of the function `f(x) = x+ sin 2x, (0 lt x lt pi)`.
Description : If a function is described by F = (3x + z, y 2 − sin x 2 z, xz + ye x5 ), then the divergence theorem value in the region 0
Last Answer : c) 39
Description : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4`
Last Answer : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4` A. ` ... 1+sqrt2)x+(sqrt2-1) pi` D. None of the above
Description : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive root
Last Answer : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the ... `1` D. third term is `(-1+sqrt(11))/(2)`
Description : `" if " int (sin 2x- cos 2x) dx=(1)/(sqrt(2)) sin (2x-k)+c " then " k=?`
Last Answer : `" if " int (sin 2x- cos 2x) dx=(1)/(sqrt(2)) sin (2x-k)+c " then " k=?` A. `-(5pi)/(4)` B. `(pi)/(4)` C. `-(pi)/(4)` 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 : \( Q: \int_{\frac{5 \pi}{4}}^{\frac{3 \pi}{2}} \frac{\frac{x}{x}-\frac{x \cdot x}{2}+\frac{(x 2)^{2}}{24}-\frac{x^{4} x 2}{720}+\cdots \infty}{\sqrt{\frac{1-\cos 2 x}{8}}} \)
Last Answer : (a) \( \infinite \) (b) \( \ln 2 \) (C) 0 (d) \( -2 \ln \sqrt{2} \) (e) \( e^{2} \)
Description : `int_(0)^(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 : `int (1)/(sqrt(sin^(3) x cos x))dx =?`
Last Answer : `int (1)/(sqrt(sin^(3) x cos x))dx =?` A. `-2sqrt(tan x) +c` B. `(2)/(sqrt(tan x)) +c` C. `(-2)/(sqrt(tan x)) +c` D.
Description : `int(sin x)/( sqrt(1+cos x))dx=?`
Last Answer : `int(sin x)/( sqrt(1+cos x))dx=?` A. `sqrt(1+cos x) +c` B. `-2sqrt(1+ cos x)+c` C. `2sqrt(1+ cos x) +c` D.
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`
Description : `int_(0)^(1) (x sin^(-1)x)/(sqrt(1+2x)^(2))dx`
Last Answer : `int_(0)^(1) (x sin^(-1)x)/(sqrt(1+2x)^(2))dx`
Description : `(i) int(1)/(sqrt(1-x^(2)).cos^(-1) x)dx` `(ii) int (sin(tan^(-1)x))/(1+x^(2))dx`
Last Answer : `(i) int(1)/(sqrt(1-x^(2)).cos^(-1) x)dx` `(ii) int (sin(tan^(-1)x))/(1+x^(2))dx`
Description : `(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx`
Last Answer : `(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx`
Description : ` (i) int sqrt(1+ sin .(x)/(2)dx)` `(ii) int (1+cos 4x)/(cot x- tan x)dx`
Last Answer : ` (i) int sqrt(1+ sin .(x)/(2)dx)` `(ii) int (1+cos 4x)/(cot x- tan x)dx`
Description : If `sin^4 alpha + 4 cos^4 beta + 2 = 4sqrt2 sin alpha cos beta ; alpha, beta in [0,pi],` then `cos(alpha+beta) - cos(alpha - beta)` is equal to :
Last Answer : If `sin^4 alpha + 4 cos^4 beta + 2 = 4sqrt2 sin alpha cos beta ; alpha, beta in [0,pi],` then `cos(alpha+beta ... sqrt(2)` B. `0` C. `sqrt(2)` D. `-1`
Description : Let `cos(alpha+beta)=(4)/(5)` and let `sin(alpha-beta)=(5)/(13)`, where `0 le alpha`, `beta=(pi)/(4)`. Then`tan2alpha=`
Last Answer : Let `cos(alpha+beta)=(4)/(5)` and let `sin(alpha-beta)=(5)/(13)`, where `0 le alpha`, `beta=(pi)/(4)`. Then ... 19)/(12)` C. `(20)/(7)` D. `(25)/(16)`
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 : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Last Answer : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Description : If `f(x)={x}+{x+[(x)/(1+x^(2))]}+{x+[(x)/(1+2x^(2))]}+{x+[(x)/(1+3x^(2))]}.......+{x+[(x)/(1+99x^(2))]}`, then values of `[f(sqrt(3))]` is where `[*]`
Last Answer : If `f(x)={x}+{x+[(x)/(1+x^(2))]}+{x+[(x)/(1+2x^(2))]}+{x+[(x)/(1+3x^(2))]} ... represent fractional part function) A. `5050` B. `4950` C. `17` D. `73`
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 : 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 : `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) 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 : `(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) 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//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) 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 : No. of solutions of `16^(sin^2x)+16^(cos^2x)=10, 0 le x le 2 pi` is
Last Answer : No. of solutions of `16^(sin^2x)+16^(cos^2x)=10, 0 le x le 2 pi` is
Description : Solve the following inequlities `(i) sqrt(x-1) lt x-3` `(ii) sqrt(x-3) gt sqrt(7-x)` `(iii) sqrt (x^(2)+4x+9) gt x +2` `(iv) 4-x lt sqrt(2x-x^(2))` `(
Last Answer : Solve the following inequlities `(i) sqrt(x-1) lt x-3` `(ii) sqrt(x-3) gt sqrt(7-x)` `(iii) sqrt (x^(2)+4x+ ... (ix) (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0`
Description : Find the maximum and minimum values of the function `f(x) = (sin x)/(1+ tan x) ,(0 lt x lt 2pi)`.
Last Answer : Find the maximum and minimum values of the function `f(x) = (sin x)/(1+ tan x) ,(0 lt x lt 2pi)`.
Description : Find the maximum and minimum values of the function `f(x) = sin x + cos 2x`.
Last Answer : Find the maximum and minimum values of the function `f(x) = sin x + cos 2x`.
Description : Find the intervals in which the function `f(x) = sin x +cos x,x in [0, 2pi]` is (i) strictly increasing, (ii) strictly decreasing.
Last Answer : Find the intervals in which the function `f(x) = sin x +cos x,x in [0, 2pi]` is (i) strictly increasing, (ii) strictly decreasing.
Description : The equation m(d 2 x/ dt 2 ) + c (dx/dt) + Kx = F 0 sin ωt is a second order differential equation. The solution of this linear equation is given as A. complementary function B. particular function C. sum of complementary and particular function D. difference of complementary and particular function
Last Answer : C. sum of complementary and particular function
Description : `int_(0)^(pi) sin 3x dx`
Last Answer : `int_(0)^(pi) sin 3x dx`
Description : Two progressive transverse waves are described by : `y_(1) = 3.0 cm sin [(4x-700t)rad]` and `y_(2) = 3.0 cm sin [(4x-700t - pi//3) rad]`.
Last Answer : Two progressive transverse waves are described by : `y_(1) = 3.0 cm sin [(4x-700t)rad]` and ... wave D. The particle will be oscillating in xy-plane.
Description : The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is
Last Answer : The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is A. `pi` B. `(pi)/(2)` C. `(3pi)/(8)` D. `(5pi)/(4)`
Description : Q. The value of is equal `sum_(k=1)^13(1/(sin(pi/4+(k-1)pi/6)sin(pi/4+k pi/6))` is equal
Last Answer : Q. The value of is equal `sum_(k=1)^13(1/(sin(pi/4+(k-1)pi/6)sin(pi/4+k pi/6))` is equal A. `3-sqrt(3)` ... (3))` C. `2(sqrt(3)-1)` D. `2(2+sqrt(3))`