Find the area under the given curves and given lines:

Question 5 of 9intermediate🔧 ApplyNumerical6 marks

(i)

$y = x^2$ , $x = 1$ , $x = 2$ and $x$ -axis

Answer

7/3 square units

(ii)

$y = x^4$ , $x = 1$ , $x = 5$ and $x$ -axis

Answer

3124/5 square units

Explanation

This question is from the Miscellaneous Exercise on Chapter 8, testing the application of finding area under simple curves. According to section 8.2, the area A of the region bounded by curve y = f(x), x-axis, and ordinates x = a and x = b is given by A = ∫ₐᵇ f(x) dx. Both curves y = x² and y = x⁴ lie above the x-axis for the given intervals, so we directly apply the integration formula.

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