A circle with centre at the origin and radius has equation
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A circle with centre at the origin and radius 3 has equation x2+y2=9. The straight line y=x intersects the circle in the first quadrant. The finite region T is enclosed by the arc of the circle in the first quadrant, the line y=x, and the y-axis.
(i) Determine the coordinates of the intersection point of y=x with the circle in the first quadrant.
(ii) Express the area of T as a definite integral (or sum of definite integrals), choosing the more convenient variable of integration and giving reasons for your choice.
(iii) Evaluate the integral(s) obtained in part (ii) and hence find the exact area of the region T.