The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted , which we can parameterize by the vector-valued function,
for , which has differential
Then with , we have
Complete the square in the quadratic term of the integrand: , then in the integral we substitute :
Make another substitution of :
Integrate by parts, taking
So, we have by the fundamental theorem of calculus that
Answer:
8 feet
Step-by-step explanation:
Given that 96 sq. feet of tile is bought to retile the bathroom.
It means area of bathroom is 96 sq. feet
Width of bathroom be x
Given that the length of the bathroom is one and a half times the width
Length of bathroom in term sod width = 1 1/2* x = 3/2 x
we know area of rectangle is given by length * width
therefore area of bathroom =( x* 3/2 x) = 3/2 x^2
Also area of bathroom is 86 sq. feet, therefore
Thus, width of bathroom is 8 feet.
Replace x and y with the given values:
2(1/8 + 4) - (3/16*8)
Use distributive property:
1/4 + 8 - (3/16 * 8)
Simplify to get final answer:
8 1/4 - 1 1/2 = 6 3/4