Answer to Question #183708 in Calculus for Sourav Mondal

Question

Integrate g(x, y) = x⁴ + y² over the region 

bounded by y = x, y = 2x and x = 2. 

Answer 1

Using double integration with respect to dydx integrate x⁴ +y² we start with dy

Integrating with respect to dy we get

x⁴y + y³/3 limit from x to 2x substituting the limit we get x⁵ +7x³/3

Then integrate with respect to dx we get x⁶/6 +7x⁴/12 substituting the limit 0-2 the solution becomes 64/6 +112/12= 240/12=20

The answer becomes 20