Answer:
x³ sin(x)
Step-by-step explanation:
Tabular method is a special form of integration by parts. It works by taking derivatives of u and integrals of dv. You multiply diagonally, then sum the results, alternating the signs.
The important thing to note is that this will produce an antiderivative only if the derivatives of u eventually become 0. So the correct choice is x³ sin(x), because the derivatives of x³ eventually becomes 0:
d/dx (x³) = 3x²
d/dx (3x²) = 6x
d/dx (6x) = 6
d/dx (6) = 0
Setting up and computing the integral is straightforward. The two parabolic cylinders 
and 
meet when
Then the volume is
Just by trying some small numbers, you discover two that work: 3 and 5.
3 + 5 = 8
3² + 5² = 9 + 25 = 34 .
gcf = 8 lcm= 5
gcf means greatest common facter. 8 goes into 8 1 time and 32 4 times. therefor 8 is the gcf. lcm means least common multiple. and 5 is the lowest number that goes into 20 and 40
A solution of a quadratic equation (ax^2+bx+c) is the point at which the parabola crosses the x-axis. We can find this by using the Quadratic formula, which is
. We can solve the equation as follows:
Then we separate the negative from -28 to get:
Then we continue to solve by factoring common terms (-2 and 2). We get the solutions of
. Choice
B matches our first solution.
:)
