Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x = 0, x = 4; about the x-axis

V= 124π/3

Step-by-step explanation:

V=∫πr²dx

This gIves:

=∫π(x+1)²dx

=∫π(x²+2x+1)dx

=π(x³/3+x²+x) |₀⁴

=π(4³/3+4²+4)-π(0³/3+0²+0)

=π(64/3+16+4)

=π(64/3+48/3+12/3)

=π(124/3)=124π/3

x is variable or an unknown value to find

example:

2x = 5 which means x = 3

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0