Find the equation of tangent to the `y = F(x)` at `x = 1`, where `F(x) = underset(x)overset(x^(3))int(dt)/(sqrt(1+t^(2)))`

Find the equation of tangent to the y = F(x) at x = 1 , where F(x) = int_(x)^(x^(3))(dt)/(sqrt(1+t^(2)))

If y = underset(u(x))overset(v(x))intf(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_((a,b)) (x-a) If F(x) = underset(1)overset(x)inte^(t^(2)//2)(1-t^(2))dt , then d/(dx) F(x) at x = 1 is

Find the equation of tangent to y=int_(x^2)^(x^3)(dt)/(sqrt(1+t^2))a tx=1.

The poins of extremum of phi(x)=underset(1)overset(x)inte^(-t^(2)//2) (1-t^(2))dt are

If f(x)=overset(x)underset(0)int(sint)/(t)dt,xgt0, then

The set of critical pionts of the fuction f(x) given by f(x)= x - log _(e)x+underset(2)overset(x)((1)/(t)-2-2cos 4t)dt is

Computing area with parametrically represented boundaries If the boundary of a figure is represented by parametric equations x = x (t) , y = y(t) , then the area of the figure is evaluated by one of the three formulae S = -underset(alpha)overset(beta)(int) y(t) x'(t) dt , S = underset(alpha) overset(beta) (int) x (t) y' (t) dt S = (1)/(2) underset(alpha)overset(beta)(int) (xy'-yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of traversal of the contour . The area enclosed by the astroid ((x)/(a))^((2)/(3)) + ((y)/(a))^((2)/(3)) = 1 is

If F(x) = int_(x^(2))^(x^(3))(1)/(lnt) dt then find F'(e )

The area bounded by y = f(x), x-axis and the line y = 1, where f(x)=1+1/x int_1^xf(t)dt is

Let g(t) = underset(x_(1))overset(x_(2))intf(t,x) dx . Then g'(t) = underset(x_(1))overset(x_(2))int(del)/(delt) (f(t,x))dx , Consider f(x) = underset(0)overset(pi)int (ln(1+xcostheta))/(costheta) d theta . The number of critical point of f(x) , in the interior of its domain, is