Consider the curve given by

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

y = \sqrt{4x - x^{2}}\,(\,y \ge 0\,)

. This curve meets the

x

-axis at

x = 0

and

x = 4

. (i) Write an integral expression for the area enclosed between the curve and the

x

-axis from

x = 0

x = 4

. (ii) By performing a suitable change of variable, evaluate the integral obtained in part (i). (iii) Hence state the exact value of the required area.

Related theory

Integration Techniques
Area Applications
Area under a curve
Area under simple curves
Applications of Integration

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