Question

integrate (20y ^ 3 + 10y) dx from 0 to 2

Answer 1

Integrate 20y³ dx

Answer 2

Since the integration is with respect to x, we can treat y as a constant. Thus, we can integrate 20y^3 with respect to x to get 20y^3x, and integrate 10y with respect to x to get 10yx. Then, we can evaluate the expression at x=2 and x=0, and subtract the two values to get the final answer.

∫(20y^3 + 10y) dx from 0 to 2
= [20y^3x + 10yx] from 0 to 2
= [20y^3(2) + 10y(2)] - [20y^3(0) + 10y(0)]
= 40y^3 + 20y - 0 - 0
= 40y^3 + 20y

Therefore, the value of the integral is 40y^3 + 20y.

Answer 3

Integrating 20y³ with respect to x means treating y as a constant and integrating with respect to x, so the integral of 20y³ dx is:

20y³x + C

where C is the constant of integration.