Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0, about the x-axis. V =

Suppose F(t) has the derivative f(t) shown below, and F(0) = 4. Find values for F(1) and F(9)

At what x values does A(x) have a local max: x = At what x values does A(x) have a local max: x=_____ Restrict your answers to values 0 < x _< 6

If the derivative f'(x) is negative, increasing, concave up Then the function f(x) is (not all info may be used): increasing, concave down decreasing, concave up decreasing, concave down increasing, concave up

For the continuous functions f(x) and g(x) in the section [Π,]], let's say that the inner product is defined as follows.

Suppose that the vector space P2 is a vector space consisting of polynomials of less than quadratic order mial f(x), g(x) >= f(x)g(x)dr is defined. d. -1 with real coefficients and that the interior of the polynomial f (a) Show that polynomials 1 and x are orthogonal. (b) Find the norm of the polynomial x. (c) Find the square above the polynomial x of polynomial x-1.

Using full sentences, write a brief summary of the geometric transformation that occurs to the integral

Ed, Jin, and Faye were debating on how to integrate the following the integral:

Luca and Maria are debating about how to evaluate the integral

The goal of this problem is to show the following integral formula holds.