अर्द्ध चक्र के लिए `I_(av)=(2I_(0))/(pi)` तथा `E_(av)=(2E_(0))/(pi)`

From the two e.m.f. Equation e_(1)=E_(0) sin (100 pi t) and e_(2)=E_(0)sin (100 pi t+(pi)/3) , we find that

If I_(I)=int_(0)^( pi/2)cos(sin x)dx,I_(2)=int_(0)^((pi)/(2))sin(cos x)d, and I_(3)=int_(0)^((pi)/(2))cos xdx then find the order in which the values I_(1),I_(2),I_(3), exist.

Let I_(1)=int_(0)^(pi//4)e^(x^(2))dx, I_(2) = int_(0)^(pi//4) e^(x)dx, I_(3) = int_(0)^(pi//4)e^(x^(2)).cos x dx , then :

Let I_(1)=int_(0)^(pi//4)e^(x^(2))dx, I_(2) = int_(0)^(pi//4) e^(x)dx, I_(3) = int_(0)^(pi//4)e^(x^(2)).sin x dx , then :

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then

(pi^(e))/(xe)+(e^(pi))/(x-pi)+(pi^(pi)+e^(e))/(x-pi-e)=0 has

int_(0)^( pi/2)e^(e^x)e^xdx=

int_ (0)^(4 pi) e^(t) (sin^(6) at+cos^(4) at) dtint_ (0)^(pi) e^(t) (sin^(6) at+ cos^(4) at) dta = 2, L = (e^(4 pi) -1)/(e^(pi) -1) (ii) a = 2, L = (e^(4 pi)+ 1)/(e^(pi) +1) (iii) a = 4, L = (e^(4 pi) -1)/(e^(pi) -1) (iv) a = 4, L = (e^(4 pi) +1)/(e^(pi) +1)