Home
Class 12
MATHS
" 21.Show that "int sqrt(a^(2)-x^(2))dx=...

" 21.Show that "int sqrt(a^(2)-x^(2))dx=(x)/(2)sqrt(a^(2)-x^(2))+(a^(2))/(2)sin^(-1)((x)/(a))+c

Promotional Banner

Similar Questions

Explore conceptually related problems

int sqrt(a^(2)-x^(2))dx=(1)/(2)x sqrt(a^(2)-x^(2))+(1)/(2)a^(2)sin^(-1)((x)/(a))+c

int(1)/(sqrt(a^(2)-x^(2)))=sin^(-1)((x)/(a))+c

Show that (d)/(dx)[(x)/(2)sqrt(a^(2)-x^(2))+(a^(2))/(2)"sin"^(-1)(x)/(a)]=sqrt(a^(2)-x^(2))

Show that int(1)/(x^(2)sqrt(a^(2)+x^(2)))dx=(-1)/(a^(2))(sqrt(a^(2)+x^(2)))/(x)+c

Show that, (d)/(dx) [(x)/(2) sqrt(a^(2)-x^(2)) +(a^(2))/(2) "sin"^(-1) (x)/(a)]=sqrt(a^(2)-x^(2))

int(dx)/(sqrt(a^(2)-x^(2)))=sin^(-1)(x/a)+C

int(1)/(sqrt(a^(2)+x^(2)))dx=log(x+sqrt(x^(2)+a^(2))+c

int(1)/(sqrt(a^2+x^2))dx=log|x+sqrt(a^2+x^2)|+c

If int sqrt(a^(2)-x^(2))dx=(x)/(2)sqrt(a^(2)-x^(2))+k sin^(-1)(x/a)+c , then the value of k is-

int(dx)/(sqrt(1-x^(2))(sin^(-1)x)^(2))