Between and (radians) the graphs of and intersect several times and enclose more than…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Between x=0 and x=2π (radians) the graphs of y=sinx and y=cosx intersect several times and enclose more than one bounded region.
(i) Find all x-coordinates in the interval [0,2π] at which the curves y=sinx and y=cosx intersect.
(ii) Using these points, formulate the necessary definite integral(s) and evaluate them to obtain the total area of all regions enclosed between the two curves over 0≤x≤2π. Give the result correct to three decimal places.