- #1
theaviator
- 6
- 0
Y=4 x=2
∫ ∫ Sinx ∕ x^2 dx dy
Y=0 x=√y
∫ ∫ Sinx ∕ x^2 dx dy
Y=0 x=√y
Integrating Sinx/x^2 from Y=4 to Y=0 with x=2 and x=√y means finding the area under the curve of the function Sinx/x^2 within the given boundaries of Y=4 and Y=0, with x values ranging from 2 to √y.
This type of integration is important because it allows us to calculate the total area under a curve, which has many real-world applications such as calculating velocity, distance, and displacement.
The general process for integrating a function involves finding the anti-derivative of the function, then applying the boundaries to calculate the definite integral.
Using a definite integral in this problem allows us to find the exact value of the area under the curve within the given boundaries, as opposed to an indefinite integral which gives us a general function.
The result of this integration can be interpreted as the total area under the curve of the function Sinx/x^2 between the boundaries of Y=4 and Y=0, with x values ranging from 2 to √y. It can also be interpreted as the exact value of the integral of the function within these boundaries.