SOLUTION: Find the area of the region in the first quadrant bounded by the line y=3x, the line x=5, the curve y={{{3/x^2}}}, and the x-axis.

Algebra ->  Surface-area -> SOLUTION: Find the area of the region in the first quadrant bounded by the line y=3x, the line x=5, the curve y={{{3/x^2}}}, and the x-axis.      Log On


   

Question 1155132: Find the area of the region in the first quadrant bounded by the line y=3x, the line x=5, the curve y=3%2Fx%5E2, and the x-axis.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


the area 3x from 0 to 1 is a right triangle , length of its legs are 1 and 3
=> the area is: 3%2A1%2F2=3%2F2=1.5+
then,take integral of 3%2Fx%5E2 from 1 to 5

int%281-%3E5%29+%283%2Fx%5E2%29%2Adx%29...take the constant out
3%2Aint%281-%3E5%29+%281%2Fx%5E2%29%2Adx%29.......1%2Fx%5E2=x%5E-2
3%2Aint%281-%3E5%29+%28x%5E-2%29%2Adx%29
3%2A%284%2F5%29
12%2F5%29
2.4%29

total area: 1.5%2B2.4=3.9+