∫√Q dx

Illustration Based upon ∫√ ax2+bx+c dx, ∫(px+q)√ax2+bx+c dx and ∫px2+qx+r/ax2+bx+c

If x=a cos q,y=b sin q, then dy/dx=

Evaluate: int(1)/(p+q tan x)dx

If x^(p)y^(q)=(x+y)^(p+q) , show that dy/dx=y/x .

Show that int_(0)^(p+q pi)|cos x|dx=2q+sin p where q in N&-(pi)/(2)

If P=int_0^oo(x^2)/(1+x^4)dx ; Q=int_0^oo(x dx)/(1+x^4)"and"R=int_0^oo(dx)/(1+x^4), then prove that :

If x^py^q=(x+y)^(p+q) , then dy/dx= (a) x/y (b) y/x (c) x/(x+y) (d) y/(y+x)

if |x|<1 then d(dx)[1+(p)/(q)x+(p(p+q))/(2!)((x)/(q))^(2)+

If the equations x^2+p x+q=0a n dx^2+p^(prime)x+q^(prime)=0 have a common root, then it must be equal to a. (p^(prime)-p ^(prime) q)/(q-q^(prime)) b. (q-q ')/(p^(prime)-p) c. (p^(prime)-p)/(q-q^(prime)) d. (p q^(prime)-p^(prime) q)/(p-p^(prime))

Evaluate the following integrals (i) int_(R)^(oo)(GMm)/(x^(2))dx (ii) int_(r_(1))^(r_(2))-k(q_(1)q_(2))/(x^(2))dx (iii) int_(u)^(v)Mvdv (iv) int_(0)^(oo)x^(-1//2)dx (v) int_(0)^(pi//2)sin x dx (vi) int_(0)^(pi//2)cos x dx (vii) int_(-pi//2)^(pi//2) cos x dx