Find the area between the curves.
$y = x^{\frac{11}{10}}, y = 9 x^{\frac{1}{10}}$
The area between the curves is (Type an exact answer.)

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The area between the curves $y = x^{\frac{11}{10}}$ and $y = 9 x^{\frac{1}{10}}$ is $43.6814745059987$ .

Steps

Step 1 ：Set the two functions equal to each other to find the points of intersection: $x^{\frac{11}{10}} = 9 x^{\frac{1}{10}}$ .

Step 2 ：The points of intersection are $x = 0.0$ and $x = 9.0$ .

Step 3 ：The area between the two curves is given by the integral of the absolute difference of the two functions over the interval defined by the points of intersection.

Step 4 ：Evaluate the integral: $\int_{0.0}^{9.0} | 9 x^{\frac{1}{10}} - x^{\frac{11}{10}} | d x$ .

Step 5 ：The area between the curves is approximately 43.6814745059987.

Step 6 ：Final Answer: The area between the curves $y = x^{\frac{11}{10}}$ and $y = 9 x^{\frac{1}{10}}$ is $43.6814745059987$ .

Find the area between the curves.y=x1110,y=9x110The area between the curves is (Type an exact answer.)

Answer

Popular Problems

Find the area between the curves.
$y = x^{\frac{11}{10}}, y = 9 x^{\frac{1}{10}}$
The area between the curves is (Type an exact answer.)