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 : Prove that: `int_0^(pi//2)log|tanx+cotx|dx=pi(log)_e2`
Last Answer : Prove that: `int_0^(pi//2)log|tanx+cotx|dx=pi(log)_e2` A. `-pi log 2` B. `pi log 2` C. `(pi)/(2) log 2` 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 : 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 : Solve the following equation `(i) 5cos2theta+2cos^(2)"(theta)/(2)+1=0`, `-(pi)/(2) lt theta lt (pi)/(2)` `(ii) sin7theta+sin4theta+sintheta=0`, `0 le
Last Answer : Solve the following equation `(i) 5cos2theta+2cos^(2)"(theta)/(2)+1=0`, `-(pi)/(2) lt theta ... iii) tantheta+sectheta=sqrt(3)`, `0 le theta le 2pi`
Description : If `5(tan^2x - cos^2x)=2cos 2x + 9`, then the value of cos4x is
Last Answer : If `5(tan^2x - cos^2x)=2cos 2x + 9`, then the value of cos4x is A. `(-3)/(5)` B. `(1)/(3)` C. `(2)/(9)` D. `-(7)/(9)`
Description : Evaluate : `int_0^1x(1-x)^5dx`
Last Answer : Evaluate : `int_0^1x(1-x)^5dx`
Description : `int(1)/(sin x cos x + 2cos^(2)x)dx`
Last Answer : `int(1)/(sin x cos x + 2cos^(2)x)dx`
Description : `(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx`
Last Answer : `(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))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^a(dx)/(sqrt(a x-x^2))`
Last Answer : `int_0^a(dx)/(sqrt(a x-x^2))`
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//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//6) sqrt(1-sin 2x) dx`
Last Answer : `int_(0)^(pi//6) sqrt(1-sin 2x) 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 : `"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 the integrals `int0pi/2(sinx)/(1+cos^2x)dx`
Last Answer : Evaluate the integrals `int0pi/2(sinx)/(1+cos^2x)dx`
Description : Evaluate: `int(2x+5)/(sqrt(x^2+2x+5)) dx`
Last Answer : Evaluate: `int(2x+5)/(sqrt(x^2+2x+5)) dx`
Description : Evaluate: `int(2x-5)sqrt(2+3x-x^2)dx`
Last Answer : Evaluate: `int(2x-5)sqrt(2+3x-x^2)dx`
Description : Evaluate : `int(2x-3)/(x^2+ 3x-18) dx`
Last Answer : Evaluate : `int(2x-3)/(x^2+ 3x-18) dx`
Description : Evaluate: `int1/(2x^2-x-1)dx`
Last Answer : Evaluate: `int1/(2x^2-x-1)dx`
Description : Evaluate: `inte^x ((sinxcosx-1)/(sin^2x)) dx`
Last Answer : Evaluate: `inte^x ((sinxcosx-1)/(sin^2x)) dx`
Description : Evaluate `int e^(2x) sin 3x dx`.
Last Answer : Evaluate `int e^(2x) sin 3x dx`.
Description : Evaluate: (i) `int(e^x)/(sqrt(4-e^(2x))) dx` (ii) `int(x^2)/(sqrt(1-x^6)) dx`
Last Answer : Evaluate: (i) `int(e^x)/(sqrt(4-e^(2x))) dx` (ii) `int(x^2)/(sqrt(1-x^6)) dx`
Description : Evaluate: (i) `int(sinx)/(1+cos^2x) dx` (ii) `int(2x^3)/(4+x^8) dx`
Last Answer : Evaluate: (i) `int(sinx)/(1+cos^2x) dx` (ii) `int(2x^3)/(4+x^8) dx`
Description : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , then `lambda` can be equal to 0
Last Answer : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , ... -1 B. 0 C. `(1)/(2)` D. 1
Description : Find the electric field when the magnetic field is given by 2sin t in air. a) 8π x 10 -7 cos t b) 4π x 10 -7 sin t c) -8π x 10 -7 cos t d) -4π x 10 -7 sin t
Last Answer : a) 8π x 10 -7 cos t
Description : V=100Sin (1000t+46 deg), I=2Sin (1000t+80 deg) what are the elements in the circuit a) R=30 ohm, L=30 mH b) R=30 ohm, C=33.3 micro farads c) R=40 ohm, L=30 mH d) R=40 ohm, L=33.3 micro farads
Last Answer : Ans: R=40 ohm, L=33.3 micro farads
Description : Evaluate : `int_(pi/3)^(pi/4)(tanx+cotx)^2dx`
Last Answer : Evaluate : `int_(pi/3)^(pi/4)(tanx+cotx)^2dx`
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 : 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 : Evaluate each of the following using identities: (i) (2x –1x)2 (ii) (2x + y) (2x – y) (iii) (a2b – b2a)2 (iv) (a – 0.1) (a + 0.1) (v) (1.5.x2 – 0.3y2) (1.5x2 + 0.3y2) -Maths 9th
Last Answer : (i) (2x - 1/x)2 [Use identity: (a - b)2 = a2 + b2 - 2ab ] (2x - 1/x)2 = (2x) 2 + (1/x)2 - 2 (2x)(1/x) = 4x2 + 1/x2 - 4 (ii) (2x + y) (2x - y) [Use identity: (a - b)(a + b) = a2 - b 2 ] (2x + y) (2x - ... ) = a2 - b 2 ](1.5 x 2 - 0.3y2 ) (1.5x2 + 0.3y2 ) = (1.5 x 2 ) 2 - (0.3y2 ) 2 = 2.25 x4 - 0.09y4
Description : Evaluate: `lim_(x rarr 1) [(x^(4)-2x^(3)-x^(2)+2x)/(x-1)]`.
Last Answer : Evaluate: `lim_(x rarr 1) [(x^(4)-2x^(3)-x^(2)+2x)/(x-1)]`.
Description : Evaluate: `lim_(x rarr oo) (x^(5)+3x^(4)-4x^(3)-3x^(2)+2x+1)/(2x^(5)+4x^(2)-9x+16)`.
Last Answer : Evaluate: `lim_(x rarr oo) (x^(5)+3x^(4)-4x^(3)-3x^(2)+2x+1)/(2x^(5)+4x^(2)-9x+16)`.
Description : Evaluate: `lim_(x rarr 2) [(2x^(2)-9x+10)/(5x^(2)-5x-10)]`.
Last Answer : Evaluate: `lim_(x rarr 2) [(2x^(2)-9x+10)/(5x^(2)-5x-10)]`.
Description : Evaluate `lim_(x rarr 2) (2x-2)`.
Last Answer : Evaluate `lim_(x rarr 2) (2x-2)`.
Description : Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−5)?
Last Answer : 104
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//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)^(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`