Find the area under the given curves and given lines:(i) `y=x^2,``x = 1, x = 2`and x-axis(ii) `y=x^4`, `x = 1, x = 5`and x-axis

Explanation

To find the area under the given curves and lines, we will solve the two parts of the question step by step.

### Part (i): Area under the curve \(y = x^2\), between \(x = 1\), \(x = 2\), and the x-axis.

1. **Identify the function and limits**: We have the function \(y = x^2\) and we need to find the area between \(x = 1\) and \(x = 2\) along with the x-axis.

2. **Set up the integral**: The area \(A\) can be calculated using the definite integral:
\[
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