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 \( y = x^2 \) from \( x = 1 \) to \( x = 2 \)

1. **Identify the function and limits**: The function is \( y = x^2 \) and the limits of integration are from \( x = 1 \) to \( x = 2 \).

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