The area under the curve y = x⁴ and the lines x = 1, x = 5 and x-axis is:

Concept:

The area under the function y = f(x) from x = a to x = b and the x-axis is given by the definite integral 

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This is for curves that are entirely on the same side of the x-axis in the given range.

If the curves are on both sides of the x-axis, then we calculate the areas of both sides separately and add them.

Definite integral: If ∫ f(x) dx = g(x) + C, then 

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Calculation:

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Using the above concept for area of a curve, we can say that the required area is:

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