Consider the following statement : `S_(1)` : The value of `int_(0)^(2pi)cos^(-1)(cosx)` dx is `pi^(2)` `S_(2)` : Area enclosed by the curve `|x-2| + |y+1| = 1` is equal to `3 sq`. Unit `S_(3)` : If `d/dx f(x) = g(x)` for `a le x le b`, then `int_(a)^(b)f(x)g(x)dx` equals to `([f(b)]^(2)-[f(a)]^(2))/(2)`. `S_(4)` : Area of the region `R = {(x,y), x^(2) le y le x}` is `1/6` State, in order, whether `S_(1), S_(2), S_(3), S_(4)` are true or falseA. `"TFTT"`B. `"TTTT"`C. `"FFFF"`D. `"TFTF"`

Consider the following statement : `S_(1)` : The value of `int_(0)^(2p

1.	Consider the following statement : `S_(1)` : The value of `int_(0)^(2pi)cos^(-1)(cosx)` dx is `pi^(2)` `S_(2)` : Area enclosed by the curve `\|x-2\| + \|y+1\| = 1` is equal to `3 sq`. Unit `S_(3)` : If `d/dx f(x) = g(x)` for `a le x le b`, then `int_(a)^(b)f(x)g(x)dx` equals to `([f(b)]^(2)-[f(a)]^(2))/(2)`. `S_(4)` : Area of the region `R = {(x,y), x^(2) le y le x}` is `1/6` State, in order, whether `S_(1), S_(2), S_(3), S_(4)` are true or falseA. `"TFTT"`B. `"TTTT"`C. `"FFFF"`D. `"TFTF"`
Answer» Correct Answer - A

Consider the integral `I=int_(0)^(2pi)(dx)/(5-2cosx)` Making the substitution `"tan"1/2x=t`, we have `I=int_(0)^(2pi)(dx)/(5-2cosx)=int_(0)^(0)(2dt)/((1+t^(2))[5-2(1-t^(2))//(1+t^(2))])=0` The result is obviously wrong, since the integrand is positive and consequently the integral of this function cannot be equal to zero. Find the mistake.
The area bounded by the curves `y=cosx` and `y=sinx` between the ordinates `x=0` and `x=(3pi)/2` isA. `4sqrt(2) + 2`B. `4sqrt(2) +1`C. `4sqrt(2) + 1`D. `4sqrt(2) - 2`
Obtain the area enclosed by region bounded by the curves `y = x ln x` and ` y = 2x-2x^(2)`.A. `7//6`B. `7//24`C. `12//7`D. `7//12`
If `I_n=int_0^pi e^x(sinx)^n dx ,` then `(I_3)/(I_1)` is equal toA. `3//5`B. `1//5`C. `1`D. `2//5`
Prove that:`I_n=int_0^oox^(2n+1)e^-x^2dx=(n !)/2,n in Ndot`
If f(x) is continuous and `int_(0)^(9)f(x)dx=4`, then the value of the integral `int_(0)^(3)x.f(x^(2))dx` isA. 2B. 18C. 16D. 4
`lim_(trarr0) int_(0)^(2pi)(|sin(x+t)-sinx|)/(|t|)dx` equalsA. 2B. 4C. 43469D. 1
Given that `lim_(nrarroo) sum_(r=1)^(n) (log_(e)(n^(2)+r^(2))-2log_(e)n)/n = log_(e)2+pi/2-2`, then evaluate : ` lim_(nrarroo) (1)/(n^(2m))[(n^(2)+1^(2))^(m)(n^(2)+2^(2))^(m) "......"(2n^(2))^(m)]^(1//n)`.
`lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))`
`lim_(nrarroo) (((n+1)(n+2)"........"3n)/(n^(2n)))^(1//n)` is equal to :A. `(27)/(e^(2))`B. `(9)/(e^(2))`C. `3 log3-2`D. `(18)/(e^(4))`