The curves x = y^ 2 +2y+3 and x = 7 - y enclose a region
MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The curves
x=y2+2y+3andx=7−y
enclose a region R.
(i) By means of a sketch, decide whether integrating with respect to x or with respect to y leads to a single definite integral for the area of R. State one reason for your choice.
(ii) Determine the coordinates of the points of intersection of the two curves.
(iii) Using the variable of integration chosen in part (i), set up and evaluate the definite integral that gives the exact area of the region R.